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 |
686.2-a1 |
686.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{10} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.136251981$ |
2.008628703 |
\( -\frac{2968038}{7} a - \frac{133931057}{224} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -44 a - 6\) , \( -66 a - 135\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-44a-6\right){x}-66a-135$ |
686.2-a2 |
686.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{5} \cdot 7^{11} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.136251981$ |
2.008628703 |
\( \frac{199003633361573}{392} a + \frac{35179204742368}{49} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -304 a - 646\) , \( -4930 a - 6831\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-304a-646\right){x}-4930a-6831$ |
686.2-b1 |
686.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{2} \cdot 7^{7} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.050461553$ |
$20.34834318$ |
1.452127213 |
\( -\frac{7974621}{686} a - \frac{12367339}{686} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -6 a - 8\) , \( 6 a + 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-8\right){x}+6a+10$ |
686.2-b2 |
686.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{6} \cdot 7^{13} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.016820517$ |
$2.260927020$ |
1.452127213 |
\( \frac{59405903367}{322828856} a + \frac{391232728667}{322828856} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 24 a + 47\) , \( 66 a + 71\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(24a+47\right){x}+66a+71$ |
686.2-c1 |
686.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{2} \cdot 7^{5} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.125216197$ |
$8.219192181$ |
1.455474647 |
\( \frac{341511377481251}{686} a - \frac{482970021761709}{686} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 30 a - 50\) , \( -122 a + 124\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(30a-50\right){x}-122a+124$ |
686.2-c2 |
686.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{6} \cdot 7^{3} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.041738732$ |
$24.65757654$ |
1.455474647 |
\( \frac{208183}{56} a - \frac{292563}{56} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}$ |
686.2-d1 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{36} \cdot 7^{8} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.661753152$ |
2.105685636 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 681 a - 1536\) , \( -19223 a + 21843\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(681a-1536\right){x}-19223a+21843$ |
686.2-d2 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{4} \cdot 7^{8} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.955778371$ |
2.105685636 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( a - 6\) , \( 5 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a-6\right){x}+5a-7$ |
686.2-d3 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{12} \cdot 7^{12} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.985259457$ |
2.105685636 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -19 a + 39\) , \( -127 a + 143\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-19a+39\right){x}-127a+143$ |
686.2-d4 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2 \cdot 7^{11} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.488944592$ |
2.105685636 |
\( -\frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -485 a - 759\) , \( 2705 a + 3591\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-485a-759\right){x}+2705a+3591$ |
686.2-d5 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{6} \cdot 7^{18} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.985259457$ |
2.105685636 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 141 a - 321\) , \( -1535 a + 1743\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(141a-321\right){x}-1535a+1743$ |
686.2-d6 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{3} \cdot 7^{21} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.985259457$ |
2.105685636 |
\( -\frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 2591 a - 4241\) , \( -94831 a + 138943\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(2591a-4241\right){x}-94831a+138943$ |
686.2-d7 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{9} \cdot 7^{11} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.661753152$ |
2.105685636 |
\( -\frac{218768831290078842857759125}{76832} a + \frac{9668307757341907702465000}{2401} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -103060 a - 164599\) , \( -23909933 a - 32816619\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-103060a-164599\right){x}-23909933a-32816619$ |
686.2-d8 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{2} \cdot 7^{10} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.955778371$ |
2.105685636 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 41 a - 96\) , \( 269 a - 307\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(41a-96\right){x}+269a-307$ |
686.2-d9 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{3} \cdot 7^{21} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.496314864$ |
2.105685636 |
\( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 251 a - 2161\) , \( 5169 a - 37057\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(251a-2161\right){x}+5169a-37057$ |
686.2-d10 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{18} \cdot 7^{10} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.661753152$ |
2.105685636 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10921 a - 24576\) , \( -1213207 a + 1378643\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(10921a-24576\right){x}-1213207a+1378643$ |
686.2-d11 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2 \cdot 7^{11} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.955778371$ |
2.105685636 |
\( \frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -134 a - 376\) , \( 1907 a + 2353\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-134a-376\right){x}+1907a+2353$ |
686.2-d12 |
686.2-d |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{9} \cdot 7^{11} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.165438288$ |
2.105685636 |
\( \frac{218768831290078842857759125}{76832} a + \frac{9668307757341907702465000}{2401} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -37479 a - 93056\) , \( -8696055 a - 9208877\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-37479a-93056\right){x}-8696055a-9208877$ |
686.2-e1 |
686.2-e |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{2} \cdot 7^{11} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.348888885$ |
2.220315274 |
\( \frac{341511377481251}{686} a - \frac{482970021761709}{686} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 478 a - 695\) , \( 6733 a - 9853\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(478a-695\right){x}+6733a-9853$ |
686.2-e2 |
686.2-e |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{6} \cdot 7^{9} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$3.139999973$ |
2.220315274 |
\( \frac{208183}{56} a - \frac{292563}{56} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 8 a - 5\) , \( 15 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-5\right){x}+15a-5$ |
686.2-f1 |
686.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{4} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.016296194$ |
1.066421746 |
\( -\frac{2968038}{7} a - \frac{133931057}{224} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -9 a - 7\) , \( -16 a - 19\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-7\right){x}-16a-19$ |
686.2-f2 |
686.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{5} \cdot 7^{5} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.016296194$ |
1.066421746 |
\( \frac{199003633361573}{392} a + \frac{35179204742368}{49} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 176 a - 256\) , \( -36 a + 32\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(176a-256\right){x}-36a+32$ |
686.2-g1 |
686.2-g |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{2} \cdot 7^{13} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$3.130511611$ |
2.213605989 |
\( -\frac{7974621}{686} a - \frac{12367339}{686} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -14 a - 39\) , \( 67 a + 51\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-14a-39\right){x}+67a+51$ |
686.2-g2 |
686.2-g |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
686.2 |
\( 2 \cdot 7^{3} \) |
\( 2^{6} \cdot 7^{19} \) |
$1.29349$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.043503870$ |
2.213605989 |
\( \frac{59405903367}{322828856} a + \frac{391232728667}{322828856} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 36 a + 216\) , \( 64 a + 756\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(36a+216\right){x}+64a+756$ |
*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.