| 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 |
| 121.1-a1 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$0.51333$ |
$(11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.370308724$ |
0.427595683 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 124.1-a1 |
124.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{50} \cdot 31 \) |
$0.51648$ |
$(-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.368431786$ |
0.425428381 |
\( -\frac{936087656892551}{1040187392} a + \frac{51401239062153}{520093696} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 1300 a - 550\) , \( -9800 a - 7280\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(1300a-550\right){x}-9800a-7280$ |
| 124.2-a1 |
124.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
124.2 |
\( 2^{2} \cdot 31 \) |
\( 2^{50} \cdot 31 \) |
$0.51648$ |
$(6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.368431786$ |
0.425428381 |
\( \frac{936087656892551}{1040187392} a - \frac{833285178768245}{1040187392} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -1301 a + 751\) , \( 10550 a - 16530\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1301a+751\right){x}+10550a-16530$ |
| 283.1-a1 |
283.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
283.1 |
\( 283 \) |
\( 283 \) |
$0.63481$ |
$(19a-13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.020644019$ |
$8.749902689$ |
0.417154410 |
\( \frac{4374}{283} a + \frac{9477}{283} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-{x}-a$ |
| 283.2-a1 |
283.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
283.2 |
\( 283 \) |
\( 283 \) |
$0.63481$ |
$(19a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.020644019$ |
$8.749902689$ |
0.417154410 |
\( -\frac{4374}{283} a + \frac{13851}{283} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-a{x}$ |
| 379.1-a1 |
379.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
379.1 |
\( 379 \) |
\( 379 \) |
$0.68290$ |
$(22a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.026097731$ |
$8.419977107$ |
0.507473108 |
\( -\frac{113062}{379} a + \frac{420487}{379} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}$ |
| 379.2-a1 |
379.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
379.2 |
\( 379 \) |
\( 379 \) |
$0.68290$ |
$(22a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.026097731$ |
$8.419977107$ |
0.507473108 |
\( \frac{113062}{379} a + \frac{307425}{379} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}$ |
| 412.1-a1 |
412.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
412.1 |
\( 2^{2} \cdot 103 \) |
\( 2^{4} \cdot 103 \) |
$0.69731$ |
$(11a-9), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.014974092$ |
$7.480035602$ |
0.517337002 |
\( -\frac{22599}{412} a + \frac{272349}{412} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -a + 1\) , \( -a\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+1\right){x}-a$ |
| 412.2-a1 |
412.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
412.2 |
\( 2^{2} \cdot 103 \) |
\( 2^{4} \cdot 103 \) |
$0.69731$ |
$(11a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.014974092$ |
$7.480035602$ |
0.517337002 |
\( \frac{22599}{412} a + \frac{124875}{206} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}$ |
| 417.1-a2 |
417.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
417.1 |
\( 3 \cdot 139 \) |
\( 3 \cdot 139^{7} \) |
$0.69941$ |
$(-2a+1), (13a-10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$1$ |
\( 1 \) |
$1$ |
$0.679671319$ |
0.784816838 |
\( -\frac{5784159447534727168}{3007633105288137} a + \frac{12389868329444077568}{3007633105288137} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 72 a + 68\) , \( 400 a - 400\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(72a+68\right){x}+400a-400$ |
| 417.2-a2 |
417.2-a |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
417.2 |
\( 3 \cdot 139 \) |
\( 3 \cdot 139^{7} \) |
$0.69941$ |
$(-2a+1), (13a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$1$ |
\( 1 \) |
$1$ |
$0.679671319$ |
0.784816838 |
\( \frac{5784159447534727168}{3007633105288137} a + \frac{6605708881909350400}{3007633105288137} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -72 a + 140\) , \( -401 a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-72a+140\right){x}-401a$ |
| 532.2-a2 |
532.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.2 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{30} \cdot 7 \cdot 19^{5} \) |
$0.74332$ |
$(-3a+1), (-5a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.617493569$ |
0.713020157 |
\( -\frac{17508172680631}{567957684224} a + \frac{5262114656059}{567957684224} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 7 a + 28\) , \( -595 a + 87\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a+28\right){x}-595a+87$ |
| 532.3-a2 |
532.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.3 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{30} \cdot 7 \cdot 19^{5} \) |
$0.74332$ |
$(3a-2), (-5a+3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.617493569$ |
0.713020157 |
\( \frac{17508172680631}{567957684224} a - \frac{3061514506143}{141989421056} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -7 a + 35\) , \( 595 a - 508\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-7a+35\right){x}+595a-508$ |
| 553.2-a1 |
553.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
553.2 |
\( 7 \cdot 79 \) |
\( 7 \cdot 79 \) |
$0.75055$ |
$(-3a+1), (10a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.032459368$ |
$8.244746797$ |
0.618040249 |
\( \frac{45056}{553} a + \frac{65536}{553} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 0\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}-a$ |
| 553.3-a1 |
553.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
553.3 |
\( 7 \cdot 79 \) |
\( 7 \cdot 79 \) |
$0.75055$ |
$(3a-2), (10a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.032459368$ |
$8.244746797$ |
0.618040249 |
\( -\frac{45056}{553} a + \frac{110592}{553} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}$ |
| 673.1-a1 |
673.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
673.1 |
\( 673 \) |
\( 673 \) |
$0.78832$ |
$(29a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.039416036$ |
$7.914920287$ |
0.720474911 |
\( -\frac{950272}{673} a + \frac{688128}{673} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(a-1\right){x}$ |
| 673.2-a1 |
673.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
673.2 |
\( 673 \) |
\( 673 \) |
$0.78832$ |
$(-29a+21)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.039416036$ |
$7.914920287$ |
0.720474911 |
\( \frac{950272}{673} a - \frac{262144}{673} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-a{x}-a$ |
| 676.2-a1 |
676.2-a |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 13^{14} \) |
$0.78920$ |
$(-4a+1), (4a-3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.3 |
$1$ |
\( 1 \) |
$1$ |
$0.560128502$ |
0.646780683 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-213{x}-1257$ |
| 679.2-a1 |
679.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
679.2 |
\( 7 \cdot 97 \) |
\( 7 \cdot 97 \) |
$0.79007$ |
$(-3a+1), (-11a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.034929906$ |
$7.994668168$ |
0.644907208 |
\( \frac{71037}{679} a + \frac{993465}{679} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}$ |
| 679.3-a1 |
679.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
679.3 |
\( 7 \cdot 97 \) |
\( 7 \cdot 97 \) |
$0.79007$ |
$(3a-2), (-11a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.034929906$ |
$7.994668168$ |
0.644907208 |
\( -\frac{71037}{679} a + \frac{1064502}{679} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}$ |
| 721.2-a1 |
721.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
721.2 |
\( 7 \cdot 103 \) |
\( 7^{2} \cdot 103 \) |
$0.80202$ |
$(-3a+1), (11a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.024305426$ |
$6.476558615$ |
0.727071148 |
\( -\frac{16418226}{5047} a + \frac{20582839}{5047} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( a - 1\) , \( a - 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(a-1\right){x}+a-1$ |
| 721.3-a1 |
721.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
721.3 |
\( 7 \cdot 103 \) |
\( 7^{2} \cdot 103 \) |
$0.80202$ |
$(3a-2), (11a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.024305426$ |
$6.476558615$ |
0.727071148 |
\( \frac{16418226}{5047} a + \frac{4164613}{5047} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -a\) , \( -a\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-a{x}-a$ |
| 723.1-a1 |
723.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
723.1 |
\( 3 \cdot 241 \) |
\( 3^{2} \cdot 241 \) |
$0.80257$ |
$(-2a+1), (-16a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.022130156$ |
$7.253556061$ |
0.741420883 |
\( -\frac{4096}{241} a + \frac{1183744}{723} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}$ |
| 723.2-a1 |
723.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
723.2 |
\( 3 \cdot 241 \) |
\( 3^{2} \cdot 241 \) |
$0.80257$ |
$(-2a+1), (16a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.022130156$ |
$7.253556061$ |
0.741420883 |
\( \frac{4096}{241} a + \frac{1171456}{723} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}-{x}-a$ |
| 784.1-CMb1 |
784.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{10} \) |
$0.81899$ |
$(-3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$1.101251020$ |
1.271615146 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( 94 a - 105\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}+94a-105$ |
| 784.3-CMb1 |
784.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
784.3 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{10} \) |
$0.81899$ |
$(3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$1.101251020$ |
1.271615146 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -94 a - 11\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-94a-11$ |
| 837.1-a1 |
837.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
837.1 |
\( 3^{3} \cdot 31 \) |
\( 3^{5} \cdot 31 \) |
$0.83249$ |
$(-2a+1), (-6a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.018108707$ |
$6.605155465$ |
0.828688140 |
\( \frac{5324}{31} a + \frac{9317}{31} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}-{x}$ |
| 837.2-a1 |
837.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
837.2 |
\( 3^{3} \cdot 31 \) |
\( 3^{5} \cdot 31 \) |
$0.83249$ |
$(-2a+1), (6a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.018108707$ |
$6.605155465$ |
0.828688140 |
\( -\frac{5324}{31} a + \frac{14641}{31} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a-1\right){x}-a$ |
| 853.1-a1 |
853.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
853.1 |
\( 853 \) |
\( 853 \) |
$0.83644$ |
$(-31a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.043284211$ |
$7.807120943$ |
0.780404537 |
\( -\frac{776012}{853} a + \frac{271697}{853} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-1\right){x}-a$ |
| 853.2-a1 |
853.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
853.2 |
\( 853 \) |
\( 853 \) |
$0.83644$ |
$(-31a+27)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.043284211$ |
$7.807120943$ |
0.780404537 |
\( \frac{776012}{853} a - \frac{504315}{853} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-{x}$ |
| 868.2-a1 |
868.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
868.2 |
\( 2^{2} \cdot 7 \cdot 31 \) |
\( 2^{10} \cdot 7^{2} \cdot 31 \) |
$0.84010$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.007690780$ |
$4.233222487$ |
0.751866768 |
\( \frac{8685387}{48608} a + \frac{17171919}{48608} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( a - 1\) , \( -a + 2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}-a+2$ |
| 868.3-a1 |
868.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
868.3 |
\( 2^{2} \cdot 7 \cdot 31 \) |
\( 2^{10} \cdot 7^{2} \cdot 31 \) |
$0.84010$ |
$(3a-2), (-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.007690780$ |
$4.233222487$ |
0.751866768 |
\( -\frac{8685387}{48608} a + \frac{12928653}{24304} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -2 a\) , \( 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-2a{x}+1$ |
| 871.2-a1 |
871.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
871.2 |
\( 13 \cdot 67 \) |
\( 13 \cdot 67 \) |
$0.84082$ |
$(-4a+1), (9a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.045788000$ |
$7.808467405$ |
0.825689652 |
\( \frac{313185}{871} a + \frac{1234186}{871} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a-1\right){x}$ |
| 871.3-a1 |
871.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
871.3 |
\( 13 \cdot 67 \) |
\( 13 \cdot 67 \) |
$0.84082$ |
$(4a-3), (9a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.045788000$ |
$7.808467405$ |
0.825689652 |
\( -\frac{313185}{871} a + \frac{1547371}{871} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$ |
| 931.2-a1 |
931.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
931.2 |
\( 7^{2} \cdot 19 \) |
\( 7^{4} \cdot 19^{2} \) |
$0.85494$ |
$(-3a+1), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cn |
$1$ |
\( 2 \cdot 3 \) |
$0.013626191$ |
$4.401623293$ |
0.831070695 |
\( -\frac{94208}{361} a + \frac{585728}{361} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 3 a - 2\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(3a-2\right){x}$ |
| 931.5-a1 |
931.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
931.5 |
\( 7^{2} \cdot 19 \) |
\( 7^{4} \cdot 19^{2} \) |
$0.85494$ |
$(3a-2), (-5a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cn |
$1$ |
\( 2 \cdot 3 \) |
$0.013626191$ |
$4.401623293$ |
0.831070695 |
\( \frac{94208}{361} a + \frac{491520}{361} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -3 a + 1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+1\right){x}-a$ |
| 961.1-CMa1 |
961.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
961.1 |
\( 31^{2} \) |
\( 31^{10} \) |
$0.86175$ |
$(-6a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$31$ |
31Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$0.802983472$ |
0.927205448 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a\) , \( 287 a - 76\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}+287a-76$ |
| 961.3-CMa1 |
961.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
961.3 |
\( 31^{2} \) |
\( 31^{10} \) |
$0.86175$ |
$(6a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$31$ |
31Cs.2.1 |
$1$ |
\( 1 \) |
$1$ |
$0.802983472$ |
0.927205448 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a\) , \( -287 a + 211\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-287a+211$ |
| 1083.2-a1 |
1083.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{2} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.037574592$ |
$5.328644115$ |
0.924784107 |
\( -\frac{1404928}{171} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -2 a + 2\) , \( 2\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-2a+2\right){x}+2$ |
| 1083.2-c1 |
1083.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{10} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.271765830$ |
1.255232601 |
\( -\frac{9358714467168256}{22284891} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -4390 a + 4390\) , \( -113432\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-4390a+4390\right){x}-113432$ |
| 1093.1-a1 |
1093.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1093.1 |
\( 1093 \) |
\( 1093 \) |
$0.88993$ |
$(36a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.050809964$ |
$7.802342922$ |
0.915531495 |
\( \frac{88373}{1093} a + \frac{28692}{1093} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-{x}$ |
| 1093.2-a1 |
1093.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1093.2 |
\( 1093 \) |
\( 1093 \) |
$0.88993$ |
$(36a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.050809964$ |
$7.802342922$ |
0.915531495 |
\( -\frac{88373}{1093} a + \frac{117065}{1093} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}-{x}$ |
| 1137.1-a1 |
1137.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1137.1 |
\( 3 \cdot 379 \) |
\( 3 \cdot 379^{5} \) |
$0.89875$ |
$(-2a+1), (22a-15)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.044593927$ |
1.206193170 |
\( -\frac{19572015114248192}{23459421833697} a + \frac{55499830713954304}{23459421833697} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -38 a + 50\) , \( -3 a - 58\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-38a+50\right){x}-3a-58$ |
| 1137.2-a1 |
1137.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1137.2 |
\( 3 \cdot 379 \) |
\( 3 \cdot 379^{5} \) |
$0.89875$ |
$(-2a+1), (22a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.044593927$ |
1.206193170 |
\( \frac{19572015114248192}{23459421833697} a + \frac{35927815599706112}{23459421833697} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 38 a + 12\) , \( 3 a - 61\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(38a+12\right){x}+3a-61$ |
| 1183.3-a1 |
1183.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1183.3 |
\( 7 \cdot 13^{2} \) |
\( 7^{6} \cdot 13^{2} \) |
$0.90771$ |
$(-3a+1), (4a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cn, 3B[2] |
$1$ |
\( 2 \) |
$0.094399864$ |
$2.099095704$ |
0.915235742 |
\( -\frac{120692215808}{117649} a - \frac{38554083328}{117649} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 30 a + 11\) , \( 52 a - 108\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(30a+11\right){x}+52a-108$ |
| 1183.3-a2 |
1183.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1183.3 |
\( 7 \cdot 13^{2} \) |
\( 7^{2} \cdot 13^{2} \) |
$0.90771$ |
$(-3a+1), (4a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cn, 3B[2] |
$1$ |
\( 2 \) |
$0.031466621$ |
$6.297287112$ |
0.915235742 |
\( -\frac{110592}{49} a + \frac{16384}{49} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( a - 1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}-a$ |
| 1183.4-a1 |
1183.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1183.4 |
\( 7 \cdot 13^{2} \) |
\( 7^{6} \cdot 13^{2} \) |
$0.90771$ |
$(3a-2), (-4a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cn, 3B[2] |
$1$ |
\( 2 \) |
$0.094399864$ |
$2.099095704$ |
0.915235742 |
\( \frac{120692215808}{117649} a - \frac{159246299136}{117649} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -30 a + 41\) , \( -53 a - 55\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-30a+41\right){x}-53a-55$ |
| 1183.4-a2 |
1183.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1183.4 |
\( 7 \cdot 13^{2} \) |
\( 7^{2} \cdot 13^{2} \) |
$0.90771$ |
$(3a-2), (-4a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cn, 3B[2] |
$1$ |
\( 2 \) |
$0.031466621$ |
$6.297287112$ |
0.915235742 |
\( \frac{110592}{49} a - \frac{94208}{49} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(a-1\right){x}$ |
| 1191.1-a1 |
1191.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1191.1 |
\( 3 \cdot 397 \) |
\( 3^{5} \cdot 397 \) |
$0.90924$ |
$(-2a+1), (-23a+12)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.016769315$ |
$5.328633650$ |
1.031811955 |
\( -\frac{3222178}{10719} a + \frac{6785567}{10719} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 2 a - 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}$ |
| 1191.2-a1 |
1191.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1191.2 |
\( 3 \cdot 397 \) |
\( 3^{5} \cdot 397 \) |
$0.90924$ |
$(-2a+1), (-23a+11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.016769315$ |
$5.328633650$ |
1.031811955 |
\( \frac{3222178}{10719} a + \frac{3563389}{10719} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}-a{x}$ |
*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.
