| 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 |
| 123627.2-a1 |
123627.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 29^{2} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.134680783$ |
$3.485517653$ |
4.336429368 |
\( -\frac{15625}{4263} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 0\) , \( 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+3$ |
| 123627.2-a2 |
123627.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{4} \cdot 7^{2} \cdot 29^{4} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.538723134$ |
$1.742758826$ |
4.336429368 |
\( \frac{4956477625}{52983} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 35 a\) , \( 66\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+35a{x}+66$ |
| 123627.2-b1 |
123627.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{6} \cdot 7^{16} \cdot 29^{2} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$2$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.614924424$ |
$0.302695113$ |
4.515615642 |
\( -\frac{53297461115137}{4513839183} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 783 a\) , \( 8720\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+783a{x}+8720$ |
| 123627.2-b2 |
123627.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{12} \cdot 7^{2} \cdot 29^{16} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$6.459697699$ |
$0.037836889$ |
4.515615642 |
\( \frac{215015459663151503}{2552757445339983} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -12482 a\) , \( 2376092\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-12482a{x}+2376092$ |
| 123627.2-b3 |
123627.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{48} \cdot 7^{2} \cdot 29^{4} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$25.83879079$ |
$0.037836889$ |
4.515615642 |
\( \frac{8471112631466271697}{1662662681263647} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 42468 a\) , \( -2756140\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+42468a{x}-2756140$ |
| 123627.2-b4 |
123627.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{24} \cdot 7^{4} \cdot 29^{8} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$6.459697699$ |
$0.075673778$ |
4.515615642 |
\( \frac{244883173420511137}{18418027974129} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 13033 a\) , \( 528806\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+13033a{x}+528806$ |
| 123627.2-b5 |
123627.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{12} \cdot 7^{8} \cdot 29^{4} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$6.459697699$ |
$0.151347556$ |
4.515615642 |
\( \frac{231331938231569617}{1472026689} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 12788 a\) , \( 551346\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+12788a{x}+551346$ |
| 123627.2-b6 |
123627.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{6} \cdot 7^{4} \cdot 29^{2} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$25.83879079$ |
$0.075673778$ |
4.515615642 |
\( \frac{947531277805646290177}{38367} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 204623 a\) , \( 35542050\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+204623a{x}+35542050$ |
| 123627.2-c1 |
123627.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{2} \cdot 7^{8} \cdot 29^{2} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.542483230$ |
$1.228973252$ |
4.377863802 |
\( \frac{90189314209}{208887} a - \frac{3189470688}{9947} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 100 a - 27\) , \( -176 a - 202\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(100a-27\right){x}-176a-202$ |
| 123627.2-c2 |
123627.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{4} \cdot 7^{10} \cdot 29^{4} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.084966461$ |
$0.614486626$ |
4.377863802 |
\( \frac{9606927435877}{43633778769} a + \frac{51585979146227}{43633778769} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 115 a - 2\) , \( -357 a + 117\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(115a-2\right){x}-357a+117$ |
| 123627.2-c3 |
123627.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{8} \cdot 7^{5} \cdot 29^{8} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.542483230$ |
$0.307243313$ |
4.377863802 |
\( -\frac{48454132677553}{137552716161} a + \frac{37022628492190}{15283635129} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -515 a - 37\) , \( -2527 a + 530\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-515a-37\right){x}-2527a+530$ |
| 123627.2-c4 |
123627.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{2} \cdot 7^{17} \cdot 29^{2} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$6.169932922$ |
$0.307243313$ |
4.377863802 |
\( -\frac{549205508488998044377}{2891264959555287} a + \frac{67727348168380070010}{963754986518429} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 985 a + 433\) , \( -9231 a + 20040\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(985a+433\right){x}-9231a+20040$ |
| 123627.2-d1 |
123627.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{2} \cdot 7^{17} \cdot 29^{2} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$6.169932922$ |
$0.307243313$ |
4.377863802 |
\( \frac{549205508488998044377}{2891264959555287} a - \frac{346023463983857834347}{2891264959555287} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 1418 a - 432\) , \( 9230 a + 10810\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1418a-432\right){x}+9230a+10810$ |
| 123627.2-d2 |
123627.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{4} \cdot 7^{10} \cdot 29^{4} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.084966461$ |
$0.614486626$ |
4.377863802 |
\( -\frac{9606927435877}{43633778769} a + \frac{6799211842456}{4848197641} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 113 a + 3\) , \( 356 a - 239\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(113a+3\right){x}+356a-239$ |
| 123627.2-d3 |
123627.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{8} \cdot 7^{5} \cdot 29^{8} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.542483230$ |
$0.307243313$ |
4.377863802 |
\( \frac{48454132677553}{137552716161} a + \frac{284749523752157}{137552716161} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -552 a + 38\) , \( 2526 a - 1996\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-552a+38\right){x}+2526a-1996$ |
| 123627.2-d4 |
123627.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
123627.2 |
\( 3 \cdot 7^{2} \cdot 29^{2} \) |
\( 3^{2} \cdot 7^{8} \cdot 29^{2} \) |
$2.90220$ |
$(-2a+1), (-3a+1), (3a-2), (29)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.542483230$ |
$1.228973252$ |
4.377863802 |
\( -\frac{90189314209}{208887} a + \frac{23210429761}{208887} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 73 a + 28\) , \( 175 a - 377\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(73a+28\right){x}+175a-377$ |
*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.
