| 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 |
| 228.1-a4 |
228.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{2} \cdot 3^{10} \cdot 19^{2} \) |
$0.60143$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$2.741115958$ |
0.633033614 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -8 a\) , \( -18 a + 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}-8a{x}-18a+8$ |
| 12996.1-b4 |
12996.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12996.1 |
\( 2^{2} \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{16} \cdot 19^{8} \) |
$1.65254$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{4} \) |
$0.763454912$ |
$0.363069678$ |
2.560546868 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 454 a - 581\) , \( -4625 a + 3099\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(454a-581\right){x}-4625a+3099$ |
| 14592.1-d4 |
14592.1-d |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14592.1 |
\( 2^{8} \cdot 3 \cdot 19 \) |
\( 2^{26} \cdot 3^{10} \cdot 19^{2} \) |
$1.70109$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.685278989$ |
1.582584036 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3 a + 150\) , \( 729 a - 378\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-3a+150\right){x}+729a-378$ |
| 33516.1-d4 |
33516.1-d |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
33516.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 2^{2} \cdot 3^{16} \cdot 7^{6} \cdot 19^{2} \) |
$2.09417$ |
$(-2a+1), (-3a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{4} \) |
$1$ |
$0.598160541$ |
2.762785196 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -87 a + 222\) , \( 925 a + 161\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-87a+222\right){x}+925a+161$ |
| 33516.5-h4 |
33516.5-h |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
33516.5 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 2^{2} \cdot 3^{16} \cdot 7^{6} \cdot 19^{2} \) |
$2.09417$ |
$(-2a+1), (3a-2), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{4} \) |
$0.676340842$ |
$0.598160541$ |
3.737168936 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 141 a - 222\) , \( 1040 a - 989\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(141a-222\right){x}+1040a-989$ |
| 38532.1-b4 |
38532.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38532.1 |
\( 2^{2} \cdot 3 \cdot 13^{2} \cdot 19 \) |
\( 2^{2} \cdot 3^{10} \cdot 13^{6} \cdot 19^{2} \) |
$2.16848$ |
$(-2a+1), (-4a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$0.911379939$ |
$0.760248780$ |
3.200254793 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 75 a - 138\) , \( -388 a + 457\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(75a-138\right){x}-388a+457$ |
| 38532.5-a4 |
38532.5-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38532.5 |
\( 2^{2} \cdot 3 \cdot 13^{2} \cdot 19 \) |
\( 2^{2} \cdot 3^{10} \cdot 13^{6} \cdot 19^{2} \) |
$2.16848$ |
$(-2a+1), (4a-3), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.760248780$ |
1.755719351 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -71 a - 68\) , \( -459 a - 96\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-71a-68\right){x}-459a-96$ |
| 43776.1-f4 |
43776.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{26} \cdot 3^{16} \cdot 19^{2} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{4} \) |
$0.993030871$ |
$0.395646009$ |
3.629350358 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -448 a + 440\) , \( 368 a - 3680\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-448a+440\right){x}+368a-3680$ |
| 43776.1-m4 |
43776.1-m |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{26} \cdot 3^{16} \cdot 19^{2} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{4} \) |
$1$ |
$0.395646009$ |
1.827410639 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 449\) , \( -359 a + 3231\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-449\right){x}-359a+3231$ |
| 142500.1-a4 |
142500.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142500.1 |
\( 2^{2} \cdot 3 \cdot 5^{4} \cdot 19 \) |
\( 2^{2} \cdot 3^{10} \cdot 5^{12} \cdot 19^{2} \) |
$3.00713$ |
$(-2a+1), (-5a+3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.1.4 |
$1$ |
\( 2^{4} \) |
$0.816458533$ |
$0.548223191$ |
4.134765571 |
\( -\frac{537398275}{175446} a + \frac{623983097}{58482} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -5 a + 234\) , \( -1363 a + 564\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-5a+234\right){x}-1363a+564$ |
*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.
