| 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 |
| 222.4-a1 |
222.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{3} \cdot 3^{6} \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$11.01686883$ |
1.387995007 |
\( -\frac{1542598609}{107892} a - \frac{4149171983}{107892} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( a - 5\) , \( 4 a - 12\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-5\right){x}+4a-12$ |
| 222.4-a2 |
222.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{9} \cdot 3^{2} \cdot 37^{3} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.224096536$ |
1.387995007 |
\( \frac{5080632565711723}{14588064} a - \frac{13442074438968901}{14588064} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 171 a - 450\) , \( 1991 a - 5267\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(171a-450\right){x}+1991a-5267$ |
| 222.4-b1 |
222.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{23} \cdot 3^{14} \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.646285252$ |
$1.829126907$ |
0.893612140 |
\( \frac{222611791066625}{724868517888} a + \frac{625719043507951}{724868517888} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 41 a + 122\) , \( -75 a - 120\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(41a+122\right){x}-75a-120$ |
| 222.4-c1 |
222.4-c |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2 \cdot 3^{2} \cdot 37^{2} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.286786960$ |
$21.13326638$ |
2.290746378 |
\( -\frac{23120355402103}{24642} a + \frac{61170758603035}{24642} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 4 a - 19\) , \( -11 a + 22\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(4a-19\right){x}-11a+22$ |
| 222.4-c2 |
222.4-c |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( - 2^{2} \cdot 3 \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.573573921$ |
$21.13326638$ |
2.290746378 |
\( \frac{43148525}{222} a + \frac{49341236}{111} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -a - 4\) , \( -2 a - 5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-a-4\right){x}-2a-5$ |
| 222.4-d1 |
222.4-d |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( - 2^{14} \cdot 3 \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.912865949$ |
0.558713315 |
\( -\frac{97298717}{14208} a + \frac{32032447}{1776} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 45 a - 119\) , \( 310 a - 824\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(45a-119\right){x}+310a-824$ |
| 222.4-d2 |
222.4-d |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{7} \cdot 3^{2} \cdot 37^{2} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.956432974$ |
0.558713315 |
\( -\frac{46690413597431}{197136} a + \frac{123585141872741}{197136} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 725 a - 1919\) , \( 18014 a - 47664\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(725a-1919\right){x}+18014a-47664$ |
| 222.4-e1 |
222.4-e |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( - 2^{4} \cdot 3^{3} \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.801929214$ |
4.385846235 |
\( \frac{2298721583}{3996} a + \frac{1520149975}{999} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 8 a - 20\) , \( 61 a - 162\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(8a-20\right){x}+61a-162$ |
| 222.4-f1 |
222.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{20} \cdot 3^{6} \cdot 37^{2} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
$0.257555913$ |
$2.964162002$ |
4.328283510 |
\( \frac{107112325}{1996002} a + \frac{174654921247}{1021953024} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -17 a + 51\) , \( -510 a + 1352\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-17a+51\right){x}-510a+1352$ |
| 222.4-f2 |
222.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{10} \cdot 3^{12} \cdot 37^{4} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \cdot 5 \) |
$0.128777956$ |
$2.964162002$ |
4.328283510 |
\( -\frac{78707600679162805}{31872191872032} a + \frac{13186758321956576}{996005996001} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 463 a - 1229\) , \( -8670 a + 22920\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(463a-1229\right){x}-8670a+22920$ |
| 222.4-f3 |
222.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{5} \cdot 3^{24} \cdot 37^{2} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
$0.257555913$ |
$2.964162002$ |
4.328283510 |
\( -\frac{211437550510753280507593}{3093168283539912} a + \frac{559440933204186860676445}{3093168283539912} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 7323 a - 19409\) , \( -558994 a + 1478996\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7323a-19409\right){x}-558994a+1478996$ |
| 222.4-f4 |
222.4-f |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{5} \cdot 3^{6} \cdot 37^{8} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
$0.257555913$ |
$0.741040500$ |
4.328283510 |
\( \frac{136037496166629488381513}{20484780175267272} a + \frac{359999892205540529594275}{20484780175267272} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1283 a - 3529\) , \( 30294 a - 80964\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1283a-3529\right){x}+30294a-80964$ |
| 222.4-g1 |
222.4-g |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( - 2^{2} \cdot 3^{13} \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.414301748$ |
2.046413707 |
\( \frac{29653341500}{58989951} a + \frac{156910190375}{117979902} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -4 a - 7\) , \( -a - 4\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-4a-7\right){x}-a-4$ |
| 222.4-h1 |
222.4-h |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( - 2^{2} \cdot 3 \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$4.851006515$ |
1.833508121 |
\( \frac{5774769294968}{111} a + \frac{30557207099105}{222} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -354 a + 934\) , \( -4958 a + 13116\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-354a+934\right){x}-4958a+13116$ |
| 222.4-i1 |
222.4-i |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( - 2^{2} \cdot 3 \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.109009488$ |
$16.92632283$ |
1.394787019 |
\( \frac{5774769294968}{111} a + \frac{30557207099105}{222} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -354 a + 937\) , \( 4604 a - 12181\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-354a+937\right){x}+4604a-12181$ |
| 222.4-j1 |
222.4-j |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( - 2^{2} \cdot 3^{13} \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 13 \) |
$0.013799592$ |
$11.24741376$ |
1.525257831 |
\( \frac{29653341500}{58989951} a + \frac{156910190375}{117979902} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -2 a - 4\) , \( -2 a - 4\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-4\right){x}-2a-4$ |
| 222.4-k1 |
222.4-k |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{20} \cdot 3^{6} \cdot 37^{2} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$2.613477818$ |
2.469504415 |
\( \frac{107112325}{1996002} a + \frac{174654921247}{1021953024} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -19 a + 48\) , \( 492 a - 1303\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-19a+48\right){x}+492a-1303$ |
| 222.4-k2 |
222.4-k |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{10} \cdot 3^{12} \cdot 37^{4} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$2.613477818$ |
2.469504415 |
\( -\frac{78707600679162805}{31872191872032} a + \frac{13186758321956576}{996005996001} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 461 a - 1232\) , \( 9132 a - 24151\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(461a-1232\right){x}+9132a-24151$ |
| 222.4-k3 |
222.4-k |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{5} \cdot 3^{24} \cdot 37^{2} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.653369454$ |
2.469504415 |
\( -\frac{211437550510753280507593}{3093168283539912} a + \frac{559440933204186860676445}{3093168283539912} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 7321 a - 19412\) , \( 566316 a - 1498407\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(7321a-19412\right){x}+566316a-1498407$ |
| 222.4-k4 |
222.4-k |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{5} \cdot 3^{6} \cdot 37^{8} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$2.613477818$ |
2.469504415 |
\( \frac{136037496166629488381513}{20484780175267272} a + \frac{359999892205540529594275}{20484780175267272} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 1281 a - 3532\) , \( -29012 a + 77433\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(1281a-3532\right){x}-29012a+77433$ |
| 222.4-l1 |
222.4-l |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( - 2^{4} \cdot 3^{3} \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.023152767$ |
$29.61345081$ |
3.109740529 |
\( \frac{2298721583}{3996} a + \frac{1520149975}{999} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 10 a - 17\) , \( -52 a + 143\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-17\right){x}-52a+143$ |
| 222.4-m1 |
222.4-m |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( - 2^{14} \cdot 3 \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.706053377$ |
$19.63608060$ |
2.620072599 |
\( -\frac{97298717}{14208} a + \frac{32032447}{1776} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 47 a - 116\) , \( -264 a + 704\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(47a-116\right){x}-264a+704$ |
| 222.4-m2 |
222.4-m |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{7} \cdot 3^{2} \cdot 37^{2} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.353026688$ |
$19.63608060$ |
2.620072599 |
\( -\frac{46690413597431}{197136} a + \frac{123585141872741}{197136} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 727 a - 1916\) , \( -17288 a + 45744\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(727a-1916\right){x}-17288a+45744$ |
| 222.4-n1 |
222.4-n |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2 \cdot 3^{2} \cdot 37^{2} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.518522611$ |
1.231884981 |
\( -\frac{23120355402103}{24642} a + \frac{61170758603035}{24642} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 4 a - 22\) , \( 15 a - 43\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(4a-22\right){x}+15a-43$ |
| 222.4-n2 |
222.4-n |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( - 2^{2} \cdot 3 \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.03704522$ |
1.231884981 |
\( \frac{43148525}{222} a + \frac{49341236}{111} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -a - 7\) , \( a - 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-7\right){x}+a-1$ |
| 222.4-o1 |
222.4-o |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{23} \cdot 3^{14} \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$1.247044839$ |
3.299370518 |
\( \frac{222611791066625}{724868517888} a + \frac{625719043507951}{724868517888} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 43 a + 125\) , \( 117 a + 241\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(43a+125\right){x}+117a+241$ |
| 222.4-p1 |
222.4-p |
$2$ |
$3$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{3} \cdot 3^{6} \cdot 37 \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.315787445$ |
$6.962986899$ |
1.662154591 |
\( -\frac{1542598609}{107892} a - \frac{4149171983}{107892} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( a - 6\) , \( -3 a + 4\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(a-6\right){x}-3a+4$ |
| 222.4-p2 |
222.4-p |
$2$ |
$3$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
222.4 |
\( 2 \cdot 3 \cdot 37 \) |
\( 2^{9} \cdot 3^{2} \cdot 37^{3} \) |
$1.82518$ |
$(a+3), (-a+2), (-3a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.105262481$ |
$6.962986899$ |
1.662154591 |
\( \frac{5080632565711723}{14588064} a - \frac{13442074438968901}{14588064} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 171 a - 451\) , \( -1820 a + 4814\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(171a-451\right){x}-1820a+4814$ |
*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.
