| 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 |
| 75.1-a7 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.235701712$ |
0.322695746 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$ |
| 1875.1-b7 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{14} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.447140342$ |
1.032626388 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2001\) , \( 34273\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2001{x}+34273$ |
| 11025.1-c7 |
11025.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.1 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (-3a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.487870110$ |
2.253375518 |
\( \frac{56667352321}{15} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 1200 a + 720\) , \( 15971 a - 30723\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1200a+720\right){x}+15971a-30723$ |
| 11025.3-c7 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.487870110$ |
2.253375518 |
\( \frac{56667352321}{15} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -718 a - 1201\) , \( -17891 a - 14032\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-718a-1201\right){x}-17891a-14032$ |
| 12675.1-a7 |
12675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.1 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.620072089$ |
2.863990301 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -639 a + 1200\) , \( 9839 a + 5397\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-639a+1200\right){x}+9839a+5397$ |
| 12675.3-a7 |
12675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.3 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (4a-3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.620072089$ |
2.863990301 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1200 a + 641\) , \( -9279 a + 14036\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1200a+641\right){x}-9279a+14036$ |
| 19200.1-g7 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.300312843$ |
$0.558925428$ |
3.356843389 |
\( \frac{56667352321}{15} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1280\) , \( -18060\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-1280{x}-18060$ |
| 57600.1-j7 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.664660740$ |
$0.322695746$ |
3.971591054 |
\( \frac{56667352321}{15} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3840 a\) , \( 108360 a - 54180\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-3840a{x}+108360a-54180$ |
| 57600.1-k7 |
57600.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.664660740$ |
$0.322695746$ |
3.971591054 |
\( \frac{56667352321}{15} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3842 a - 3841\) , \( -104519 a + 50339\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3842a-3841\right){x}-104519a+50339$ |
| 81225.1-a7 |
81225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.1 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.013853729$ |
$0.296125925$ |
2.754442525 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -1201 a - 3841\) , \( 44286 a + 89262\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1201a-3841\right){x}+44286a+89262$ |
| 81225.3-a7 |
81225.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.3 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.013853729$ |
$0.296125925$ |
2.754442525 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 3841 a + 1200\) , \( -44287 a + 133549\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(3841a+1200\right){x}-44287a+133549$ |
| 102675.1-a7 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$6.036317352$ |
$0.367547097$ |
5.123708641 |
\( \frac{56667352321}{15} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 560 a + 2641\) , \( -69511 a + 50796\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(560a+2641\right){x}-69511a+50796$ |
| 102675.3-a7 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$6.036317352$ |
$0.367547097$ |
5.123708641 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 3201 a - 2641\) , \( 69511 a - 18715\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(3201a-2641\right){x}+69511a-18715$ |
*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.
