| 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 |
| 200.2-a6 |
200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$0.67209$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$5.993777963$ |
0.749222245 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 1\) , \( i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+1\right){x}+i$ |
| 2000.2-a6 |
2000.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{4} \cdot 5^{10} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.680498993$ |
1.340249496 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -7 i - 6\) , \( -11 i + 2\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-7i-6\right){x}-11i+2$ |
| 2000.3-a6 |
2000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.3 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{4} \cdot 5^{10} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.680498993$ |
1.340249496 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 7 i - 6\) , \( -11 i - 2\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(7i-6\right){x}-11i-2$ |
| 5000.3-a6 |
5000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5000.3 |
\( 2^{3} \cdot 5^{4} \) |
\( 2^{4} \cdot 5^{16} \) |
$1.50283$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.466696751$ |
$1.198755592$ |
2.237821363 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 43\) , \( 115 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+43\right){x}+115i$ |
| 6400.2-a6 |
6400.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$1.59850$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.361102669$ |
$2.996888981$ |
2.164369220 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 7\) , \( -6 i\bigr] \) |
${y}^2={x}^{3}+7{x}-6i$ |
| 16200.2-a6 |
16200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16200.2 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.341880646$ |
$1.997925987$ |
2.732208912 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 15\) , \( 28 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+15{x}+28i$ |
| 25600.2-j6 |
25600.2-j |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{4} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.119120521$ |
2.119120521 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 14 i\) , \( 12 i + 12\bigr] \) |
${y}^2={x}^{3}+14i{x}+12i+12$ |
| 25600.2-p6 |
25600.2-p |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{4} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.119120521$ |
2.119120521 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -14 i\) , \( -12 i + 12\bigr] \) |
${y}^2={x}^{3}-14i{x}-12i+12$ |
| 32000.2-l6 |
32000.2-l |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{16} \cdot 5^{10} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.340249496$ |
2.680498993 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -28 i - 21\) , \( 66 i + 12\bigr] \) |
${y}^2={x}^{3}+\left(-28i-21\right){x}+66i+12$ |
| 32000.3-l6 |
32000.3-l |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{16} \cdot 5^{10} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.340249496$ |
2.680498993 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 28 i - 21\) , \( -66 i + 12\bigr] \) |
${y}^2={x}^{3}+\left(28i-21\right){x}-66i+12$ |
| 57800.4-e6 |
57800.4-e |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.4 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 17^{6} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.453704684$ |
2.907409369 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -14 i - 27\) , \( 22 i + 46\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-14i-27\right){x}+22i+46$ |
| 57800.6-d6 |
57800.6-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57800.6 |
\( 2^{3} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 17^{6} \) |
$2.77109$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.453704684$ |
2.907409369 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 14 i - 27\) , \( 22 i - 46\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(14i-27\right){x}+22i-46$ |
| 67600.4-d6 |
67600.4-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.4 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.129245912$ |
$1.662374906$ |
3.754460134 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -21 i + 8\) , \( 11 i - 24\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-21i+8\right){x}+11i-24$ |
| 67600.6-f6 |
67600.6-f |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.129245912$ |
$1.662374906$ |
3.754460134 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 20 i + 8\) , \( -3 i - 45\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(20i+8\right){x}-3i-45$ |
*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.
