| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 25.1-CMa1 |
25.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 5^{3} \) |
$0.39963$ |
$(-a-2)$ |
0 |
$\Z/10\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$5$ |
5Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$9.195427721$ |
0.183908554 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -i - 1\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-i-1\right){x}$ |
| 25.3-CMa1 |
25.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25.3 |
\( 5^{2} \) |
\( 5^{3} \) |
$0.39963$ |
$(2a+1)$ |
0 |
$\Z/10\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$5$ |
5Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$9.195427721$ |
0.183908554 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( i\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}$ |
| 64.1-CMa1 |
64.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$0.50549$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.875185818$ |
0.429699113 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 64.1-CMa2 |
64.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$0.50549$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{yes}$ |
$-16$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$6.875185818$ |
0.429699113 |
\( 287496 \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 2\) , \( 3 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+2{x}+3i$ |
| 65.2-a1 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5^{9} \cdot 13^{2} \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.850436644$ |
0.425218322 |
\( -\frac{157034896049234432}{330078125} a - \frac{128574568523373376}{330078125} \) |
\( \bigl[i + 1\) , \( 0\) , \( i\) , \( 239 i - 399\) , \( -2869 i + 2627\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(239i-399\right){x}-2869i+2627$ |
| 65.2-a2 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5^{6} \cdot 13^{3} \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.551309934$ |
0.425218322 |
\( -\frac{2088753403392}{34328125} a - \frac{1627055822656}{34328125} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 1\) , \( -15 i + 3\) , \( 7 i - 14\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-15i+3\right){x}+7i-14$ |
| 65.2-a3 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5^{2} \cdot 13 \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.653929802$ |
0.425218322 |
\( \frac{732672}{325} a - \frac{3306304}{325} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 1\) , \( -2\) , \( -i - 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}-2{x}-i-1$ |
| 65.2-a4 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5^{18} \cdot 13 \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.850436644$ |
0.425218322 |
\( \frac{1110974116587520512}{49591064453125} a - \frac{489671365797093184}{49591064453125} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 1\) , \( -60 i + 98\) , \( 372 i + 410\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-60i+98\right){x}+372i+410$ |
| 65.2-a5 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5 \cdot 13^{2} \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.653929802$ |
0.425218322 |
\( -\frac{1183232}{845} a - \frac{851776}{845} \) |
\( \bigl[i + 1\) , \( 0\) , \( i\) , \( -i + 1\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}$ |
| 65.2-a6 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5^{3} \cdot 13^{6} \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.551309934$ |
0.425218322 |
\( \frac{356394317312}{603351125} a + \frac{580261889216}{603351125} \) |
\( \bigl[i + 1\) , \( 0\) , \( i\) , \( 4 i - 4\) , \( -2 i + 5\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(4i-4\right){x}-2i+5$ |
| 65.3-a1 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5^{9} \cdot 13^{2} \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.850436644$ |
0.425218322 |
\( \frac{157034896049234432}{330078125} a - \frac{128574568523373376}{330078125} \) |
\( \bigl[i + 1\) , \( -i\) , \( i\) , \( -240 i - 399\) , \( 2869 i + 2627\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-240i-399\right){x}+2869i+2627$ |
| 65.3-a2 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5^{6} \cdot 13^{3} \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.551309934$ |
0.425218322 |
\( \frac{2088753403392}{34328125} a - \frac{1627055822656}{34328125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( 14 i + 4\) , \( 7 i + 14\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(14i+4\right){x}+7i+14$ |
| 65.3-a3 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5^{2} \cdot 13 \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.653929802$ |
0.425218322 |
\( -\frac{732672}{325} a - \frac{3306304}{325} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( -i - 1\) , \( -i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-i-1\right){x}-i+1$ |
| 65.3-a4 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5^{18} \cdot 13 \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.850436644$ |
0.425218322 |
\( -\frac{1110974116587520512}{49591064453125} a - \frac{489671365797093184}{49591064453125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( 59 i + 99\) , \( 372 i - 410\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(59i+99\right){x}+372i-410$ |
| 65.3-a5 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5 \cdot 13^{2} \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.653929802$ |
0.425218322 |
\( \frac{1183232}{845} a - \frac{851776}{845} \) |
\( \bigl[i + 1\) , \( -i\) , \( i\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}-i{x}^{2}+{x}$ |
| 65.3-a6 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5^{3} \cdot 13^{6} \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.551309934$ |
0.425218322 |
\( -\frac{356394317312}{603351125} a + \frac{580261889216}{603351125} \) |
\( \bigl[i + 1\) , \( -i\) , \( i\) , \( -5 i - 4\) , \( 2 i + 5\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-5i-4\right){x}+2i+5$ |
| 72.1-a1 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.817673508$ |
0.454418377 |
\( \frac{207646}{6561} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i - 4\) , \( 22 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i-4\right){x}+22i$ |
| 72.1-a2 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
0.454418377 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
| 72.1-a3 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
0.454418377 |
\( \frac{35152}{9} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 1\) , \( -i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i+1\right){x}-i$ |
| 72.1-a4 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
0.454418377 |
\( \frac{1556068}{81} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 6\) , \( -5 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+6\right){x}-5i$ |
| 72.1-a5 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.635347017$ |
0.454418377 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 16\) , \( -28 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i+16\right){x}-28i$ |
| 72.1-a6 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
0.454418377 |
\( \frac{3065617154}{9} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 96\) , \( -347 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+96\right){x}-347i$ |
| 98.1-a1 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.875417135$ |
0.437708567 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -170\) , \( 874\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-170{x}+874$ |
| 98.1-a2 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.878754216$ |
0.437708567 |
\( -\frac{15625}{28} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 0\) , \( 0\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}$ |
| 98.1-a3 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.626251405$ |
0.437708567 |
\( \frac{9938375}{21952} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 5\) , \( 6\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+5{x}+6$ |
| 98.1-a4 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.313125702$ |
0.437708567 |
\( \frac{4956477625}{941192} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -35\) , \( 70\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-35{x}+70$ |
| 98.1-a5 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.939377108$ |
0.437708567 |
\( \frac{128787625}{98} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -10\) , \( -12\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-10{x}-12$ |
| 98.1-a6 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.437708567$ |
0.437708567 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -2730\) , \( 55146\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-2730{x}+55146$ |
| 100.2-a1 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{5} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.211547828$ |
0.535257971 |
\( -\frac{59648644}{625} a - \frac{119744792}{625} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 4 i - 11\) , \( 11 i - 12\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(4i-11\right){x}+11i-12$ |
| 100.2-a2 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{5} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.211547828$ |
0.535257971 |
\( \frac{59648644}{625} a - \frac{119744792}{625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -6 i - 11\) , \( -12 i - 12\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-6i-11\right){x}-12i-12$ |
| 100.2-a3 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{15} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.070515942$ |
0.535257971 |
\( -\frac{893935595564}{244140625} a - \frac{1336401187352}{244140625} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 54 i - 1\) , \( -119 i - 118\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(54i-1\right){x}-119i-118$ |
| 100.2-a4 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{15} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.070515942$ |
0.535257971 |
\( \frac{893935595564}{244140625} a - \frac{1336401187352}{244140625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -56 i - 1\) , \( 118 i - 118\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-56i-1\right){x}+118i-118$ |
| 100.2-a5 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.141031885$ |
0.535257971 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 9\) , \( 17 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+9\right){x}+17i$ |
| 100.2-a6 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.423095656$ |
0.535257971 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 1\) , \( -i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}-i$ |
| 100.2-a7 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$6.423095656$ |
0.535257971 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}$ |
| 100.2-a8 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2.141031885$ |
0.535257971 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-116$ |
| 106.1-a1 |
106.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
106.1 |
\( 2 \cdot 53 \) |
\( 2^{9} \cdot 53 \) |
$0.57345$ |
$(a+1), (-2a+7)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$5.985343332$ |
0.665038148 |
\( -\frac{24565}{1696} a + \frac{44217}{1696} \) |
\( \bigl[1\) , \( i - 1\) , \( i + 1\) , \( -i - 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-i-1\right){x}$ |
| 106.1-a2 |
106.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
106.1 |
\( 2 \cdot 53 \) |
\( 2 \cdot 53^{9} \) |
$0.57345$ |
$(a+1), (-2a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.665038148$ |
0.665038148 |
\( \frac{2664717683643388715}{6599527183604266} a + \frac{2995316993300077017}{6599527183604266} \) |
\( \bigl[1\) , \( i - 1\) , \( i + 1\) , \( -76 i + 14\) , \( 225 i + 345\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-76i+14\right){x}+225i+345$ |
| 106.1-a3 |
106.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
106.1 |
\( 2 \cdot 53 \) |
\( 2^{3} \cdot 53^{3} \) |
$0.57345$ |
$(a+1), (-2a+7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$1.995114444$ |
0.665038148 |
\( \frac{12075196954415}{595508} a + \frac{199712312811}{595508} \) |
\( \bigl[1\) , \( i - 1\) , \( i + 1\) , \( -51 i - 31\) , \( 174 i + 30\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-51i-31\right){x}+174i+30$ |
| 106.2-a1 |
106.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
106.2 |
\( 2 \cdot 53 \) |
\( 2^{9} \cdot 53 \) |
$0.57345$ |
$(a+1), (2a+7)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$5.985343332$ |
0.665038148 |
\( \frac{24565}{1696} a + \frac{44217}{1696} \) |
\( \bigl[1\) , \( -i - 1\) , \( i + 1\) , \( -1\) , \( -i\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}-{x}-i$ |
| 106.2-a2 |
106.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
106.2 |
\( 2 \cdot 53 \) |
\( 2 \cdot 53^{9} \) |
$0.57345$ |
$(a+1), (2a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.665038148$ |
0.665038148 |
\( -\frac{2664717683643388715}{6599527183604266} a + \frac{2995316993300077017}{6599527183604266} \) |
\( \bigl[1\) , \( -i - 1\) , \( i + 1\) , \( 75 i + 14\) , \( -226 i + 345\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(75i+14\right){x}-226i+345$ |
| 106.2-a3 |
106.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
106.2 |
\( 2 \cdot 53 \) |
\( 2^{3} \cdot 53^{3} \) |
$0.57345$ |
$(a+1), (2a+7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$1.995114444$ |
0.665038148 |
\( -\frac{12075196954415}{595508} a + \frac{199712312811}{595508} \) |
\( \bigl[1\) , \( -i - 1\) , \( i + 1\) , \( 50 i - 31\) , \( -175 i + 30\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(50i-31\right){x}-175i+30$ |
| 121.1-a1 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$0.59274$ |
$(11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.370308724$ |
0.370308724 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( i\) , \( -7820\) , \( 263580\bigr] \) |
${y}^2+i{y}={x}^{3}+{x}^{2}-7820{x}+263580$ |
| 121.1-a2 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$0.59274$ |
$(11)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1.851543623$ |
0.370308724 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( i\) , \( -10\) , \( 20\bigr] \) |
${y}^2+i{y}={x}^{3}+{x}^{2}-10{x}+20$ |
| 121.1-a3 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$0.59274$ |
$(11)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$9.257718117$ |
0.370308724 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( i\) , \( 0\) , \( 0\bigr] \) |
${y}^2+i{y}={x}^{3}+{x}^{2}$ |
| 130.1-a1 |
130.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.1 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{18} \cdot 5^{9} \cdot 13 \) |
$0.60347$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.960726389$ |
0.480363194 |
\( \frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i\) , \( -i + 1\) , \( i\) , \( 89 i - 50\) , \( -368 i + 14\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(89i-50\right){x}-368i+14$ |
| 130.1-a2 |
130.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.1 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{6} \cdot 5^{3} \cdot 13^{3} \) |
$0.60347$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.882179168$ |
0.480363194 |
\( -\frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i\) , \( -i + 1\) , \( i\) , \( 9 i + 5\) , \( 2 i + 18\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(9i+5\right){x}+2i+18$ |
| 130.1-a3 |
130.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.1 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{3} \cdot 5^{6} \cdot 13^{6} \) |
$0.60347$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.441089584$ |
0.480363194 |
\( -\frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[i\) , \( -i + 1\) , \( i\) , \( -i + 15\) , \( 30 i + 30\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-i+15\right){x}+30i+30$ |
| 130.1-a4 |
130.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.1 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{9} \cdot 5^{18} \cdot 13^{2} \) |
$0.60347$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.480363194$ |
0.480363194 |
\( \frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[i\) , \( -i + 1\) , \( i\) , \( 9 i - 130\) , \( -688 i - 882\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(9i-130\right){x}-688i-882$ |
| 130.1-a5 |
130.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.1 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{2} \cdot 5 \cdot 13 \) |
$0.60347$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$8.646537506$ |
0.480363194 |
\( -\frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i\) , \( -i + 1\) , \( i\) , \( -i\) , \( 0\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}-i{x}$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
