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 |
4.1-a1 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$35.74821466$ |
2.426746937 |
\( -\frac{7861875}{64} a - \frac{26985875}{32} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4575 a + 35985\) , \( -2480637 a + 19511351\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-4575a+35985\right){x}-2480637a+19511351$ |
4.1-a2 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$35.74821466$ |
2.426746937 |
\( \frac{7861875}{64} a - \frac{61833625}{64} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 4575 a + 31410\) , \( 2480637 a + 17030714\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(4575a+31410\right){x}+2480637a+17030714$ |
4.1-a3 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$35.74821466$ |
2.426746937 |
\( -\frac{1779679887375}{8} a + \frac{13998000969625}{8} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -89895 a - 617170\) , \( 37511019 a + 257530398\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-89895a-617170\right){x}+37511019a+257530398$ |
4.1-a4 |
4.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$35.74821466$ |
2.426746937 |
\( \frac{1779679887375}{8} a + \frac{6109160541125}{4} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 89895 a - 707065\) , \( -37511019 a + 295041417\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(89895a-707065\right){x}-37511019a+295041417$ |
4.1-b1 |
4.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$32.05257343$ |
6.527611391 |
\( -\frac{2193}{8} a - \frac{2459}{4} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -5894 a - 40465\) , \( 851278 a + 5844415\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-5894a-40465\right){x}+851278a+5844415$ |
4.1-b2 |
4.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$32.05257343$ |
6.527611391 |
\( \frac{2193}{8} a - \frac{7111}{8} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 5894 a - 46359\) , \( -851278 a + 6695693\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(5894a-46359\right){x}-851278a+6695693$ |
4.1-c1 |
4.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$14.29159922$ |
2.910530915 |
\( -\frac{2193}{8} a - \frac{2459}{4} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -7682232 a + 60424288\) , \( -18970234890 a + 149209622415\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-7682232a+60424288\right){x}-18970234890a+149209622415$ |
4.1-c2 |
4.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$14.29159922$ |
2.910530915 |
\( \frac{2193}{8} a - \frac{7111}{8} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 7682232 a + 52742056\) , \( 18970234890 a + 130239387525\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(7682232a+52742056\right){x}+18970234890a+130239387525$ |
4.1-d1 |
4.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.098105599$ |
0.346081958 |
\( -\frac{7861875}{64} a - \frac{26985875}{32} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -76876685 a - 527793801\) , \( -996242529392 a - 6839663167426\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-76876685a-527793801\right){x}-996242529392a-6839663167426$ |
4.1-d2 |
4.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.098105599$ |
0.346081958 |
\( \frac{7861875}{64} a - \frac{61833625}{64} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 76876685 a - 604670486\) , \( 996242529392 a - 7835905696818\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(76876685a-604670486\right){x}+996242529392a-7835905696818$ |
4.1-d3 |
4.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$5.098105599$ |
0.346081958 |
\( -\frac{1779679887375}{8} a + \frac{13998000969625}{8} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1230190055 a - 9676010586\) , \( 63741468271084 a - 501355964650234\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(1230190055a-9676010586\right){x}+63741468271084a-501355964650234$ |
4.1-d4 |
4.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$1.86159$ |
$(-a+8), (-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$5.098105599$ |
0.346081958 |
\( \frac{1779679887375}{8} a + \frac{6109160541125}{4} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1230190055 a - 8445820531\) , \( -63741468271084 a - 437614496379150\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-1230190055a-8445820531\right){x}-63741468271084a-437614496379150$ |
6.1-a1 |
6.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3 \) |
$2.06019$ |
$(-a+8), (-52a-357)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.801985746$ |
$29.66850780$ |
3.230445974 |
\( \frac{30385}{6} a + \frac{208607}{6} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a + 18\) , \( -5 a + 9\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+18\right){x}-5a+9$ |
6.1-b1 |
6.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3 \) |
$2.06019$ |
$(-a+8), (-52a-357)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$30.54717750$ |
2.073677529 |
\( \frac{30385}{6} a + \frac{208607}{6} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -83592993998 a - 573904350815\) , \( 35287915421569989 a + 242267769386884299\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-83592993998a-573904350815\right){x}+35287915421569989a+242267769386884299$ |
6.2-a1 |
6.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{8} \) |
$2.06019$ |
$(-a+8), (-52a+409)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$16.22987535$ |
8.814045832 |
\( \frac{1333879}{13122} a + \frac{368465}{486} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 1454820719431 a + 9988013356524\) , \( 857134272549098597 a + 5884621003953910568\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(1454820719431a+9988013356524\right){x}+857134272549098597a+5884621003953910568$ |
6.2-b1 |
6.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{8} \) |
$2.06019$ |
$(-a+8), (-52a+409)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$2.451506314$ |
$9.778072031$ |
6.509031491 |
\( \frac{1333879}{13122} a + \frac{368465}{486} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 7 a + 83\) , \( 20 a + 171\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(7a+83\right){x}+20a+171$ |
6.3-a1 |
6.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{8} \) |
$2.06019$ |
$(-a-7), (-52a-357)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$16.22987535$ |
8.814045832 |
\( -\frac{1333879}{13122} a + \frac{5641217}{6561} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -1454820719433 a + 11442834075956\) , \( -857134272549098598 a + 6741755276503009165\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1454820719433a+11442834075956\right){x}-857134272549098598a+6741755276503009165$ |
6.3-b1 |
6.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{8} \) |
$2.06019$ |
$(-a-7), (-52a-357)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$2.451506314$ |
$9.778072031$ |
6.509031491 |
\( -\frac{1333879}{13122} a + \frac{5641217}{6561} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -7 a + 36\) , \( -14 a + 101\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a+36\right){x}-14a+101$ |
6.4-a1 |
6.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3 \) |
$2.06019$ |
$(-a-7), (-52a+409)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.801985746$ |
$29.66850780$ |
3.230445974 |
\( -\frac{30385}{6} a + 39832 \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 18\) , \( 4 a + 5\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+18{x}+4a+5$ |
6.4-b1 |
6.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3 \) |
$2.06019$ |
$(-a-7), (-52a+409)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$30.54717750$ |
2.073677529 |
\( -\frac{30385}{6} a + 39832 \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 83592993997 a - 657497344813\) , \( -35287915421569990 a + 277555684808454288\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(83592993997a-657497344813\right){x}-35287915421569990a+277555684808454288$ |
7.1-a1 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{12} \) |
$2.14113$ |
$(-498a+3917)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$4.009166008$ |
0.136079961 |
\( -\frac{658503}{117649} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 945951 a - 7440340\) , \( -23919915394 a + 188141136092\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(945951a-7440340\right){x}-23919915394a+188141136092$ |
7.1-a2 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{3} \) |
$2.14113$ |
$(-498a+3917)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$32.07332806$ |
0.136079961 |
\( -\frac{34063182558}{49} a + \frac{267922691739}{49} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 173213478909 a - 1362403677925\) , \( -106496592842533228 a + 837644683825909912\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(173213478909a-1362403677925\right){x}-106496592842533228a+837644683825909912$ |
7.1-a3 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$2.14113$ |
$(-498a+3917)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$16.03666403$ |
0.136079961 |
\( \frac{34965783}{343} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3555471 a - 27965415\) , \( -9820546524 a + 77243115188\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3555471a-27965415\right){x}-9820546524a+77243115188$ |
7.1-a4 |
7.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{3} \) |
$2.14113$ |
$(-498a+3917)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$8.018332017$ |
0.136079961 |
\( \frac{34063182558}{49} a + \frac{233859509181}{49} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 129 a - 1015\) , \( 656 a - 5160\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(129a-1015\right){x}+656a-5160$ |
7.1-b1 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{12} \) |
$2.14113$ |
$(-498a+3917)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$4.009166008$ |
0.136079961 |
\( -\frac{658503}{117649} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -945951 a - 6494389\) , \( 23919915394 a + 164221220698\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-945951a-6494389\right){x}+23919915394a+164221220698$ |
7.1-b2 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{3} \) |
$2.14113$ |
$(-498a+3917)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$8.018332017$ |
0.136079961 |
\( -\frac{34063182558}{49} a + \frac{267922691739}{49} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -129 a - 886\) , \( -656 a - 4504\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-129a-886\right){x}-656a-4504$ |
7.1-b3 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$2.14113$ |
$(-498a+3917)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$16.03666403$ |
0.136079961 |
\( \frac{34965783}{343} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3555471 a - 24409944\) , \( 9820546524 a + 67422568664\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3555471a-24409944\right){x}+9820546524a+67422568664$ |
7.1-b4 |
7.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( 7^{3} \) |
$2.14113$ |
$(-498a+3917)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$32.07332806$ |
0.136079961 |
\( \frac{34063182558}{49} a + \frac{233859509181}{49} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -173213478909 a - 1189190199016\) , \( 106496592842533228 a + 731148090983376684\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-173213478909a-1189190199016\right){x}+106496592842533228a+731148090983376684$ |
8.1-a1 |
8.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{29} \) |
$2.21381$ |
$(-a+8), (-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1.520883425$ |
$13.88937213$ |
2.867996848 |
\( \frac{169942716001}{2097152} a - \frac{676100323303}{1048576} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -113 a - 696\) , \( 1555 a + 10865\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-113a-696\right){x}+1555a+10865$ |
8.1-a2 |
8.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{15} \) |
$2.21381$ |
$(-a+8), (-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.506961141$ |
$13.88937213$ |
2.867996848 |
\( \frac{13657}{128} a + \frac{53585}{64} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 2 a + 94\) , \( -a + 185\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+94\right){x}-a+185$ |
8.1-b1 |
8.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{29} \) |
$2.21381$ |
$(-a+8), (-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$12.50954182$ |
$1.087722570$ |
1.847394612 |
\( \frac{169942716001}{2097152} a - \frac{676100323303}{1048576} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 1869574935893 a - 14705066746888\) , \( 3779122287683704783 a - 29724534929365231599\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1869574935893a-14705066746888\right){x}+3779122287683704783a-29724534929365231599$ |
8.1-b2 |
8.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{15} \) |
$2.21381$ |
$(-a+8), (-a-7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$4.169847275$ |
$9.789503138$ |
1.847394612 |
\( \frac{13657}{128} a + \frac{53585}{64} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -24740869992 a + 194598321582\) , \( 22630333034170967 a - 177997977712882799\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24740869992a+194598321582\right){x}+22630333034170967a-177997977712882799$ |
8.2-a1 |
8.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{29} \) |
$2.21381$ |
$(-a+8), (-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1.520883425$ |
$13.88937213$ |
2.867996848 |
\( -\frac{169942716001}{2097152} a - \frac{1182257930605}{2097152} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 114 a - 755\) , \( -1442 a + 11665\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(114a-755\right){x}-1442a+11665$ |
8.2-a2 |
8.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{15} \) |
$2.21381$ |
$(-a+8), (-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.506961141$ |
$13.88937213$ |
2.867996848 |
\( -\frac{13657}{128} a + \frac{120827}{128} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -a + 150\) , \( -a + 334\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-a+150\right){x}-a+334$ |
8.2-b1 |
8.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{29} \) |
$2.21381$ |
$(-a+8), (-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$12.50954182$ |
$1.087722570$ |
1.847394612 |
\( -\frac{169942716001}{2097152} a - \frac{1182257930605}{2097152} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -1869574935895 a - 12835491810995\) , \( -3779122287683704784 a - 25945412641681526816\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-1869574935895a-12835491810995\right){x}-3779122287683704784a-25945412641681526816$ |
8.2-b2 |
8.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{15} \) |
$2.21381$ |
$(-a+8), (-a-7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$4.169847275$ |
$9.789503138$ |
1.847394612 |
\( -\frac{13657}{128} a + \frac{120827}{128} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 24740869990 a + 169857451590\) , \( -22630333034170968 a - 155367644678711832\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(24740869990a+169857451590\right){x}-22630333034170968a-155367644678711832$ |
8.3-a1 |
8.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{11} \) |
$2.21381$ |
$(-a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.783342260$ |
$18.65119014$ |
1.983618890 |
\( 122654 a - 964730 \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( 5238176497 a + 35962490874\) , \( -66537844035834579 a - 456812902144981867\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5238176497a+35962490874\right){x}-66537844035834579a-456812902144981867$ |
8.3-b1 |
8.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{11} \) |
$2.21381$ |
$(-a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.389807035$ |
$6.932125642$ |
1.308040105 |
\( 122654 a - 964730 \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( 17 a - 118\) , \( 63 a - 499\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(17a-118\right){x}+63a-499$ |
8.4-a1 |
8.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{11} \) |
$2.21381$ |
$(-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.783342260$ |
$18.65119014$ |
1.983618890 |
\( -122654 a - 842076 \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -5238176497 a + 41200667371\) , \( 66537844035834578 a - 523350746180816446\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-5238176497a+41200667371\right){x}+66537844035834578a-523350746180816446$ |
8.4-b1 |
8.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{11} \) |
$2.21381$ |
$(-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.389807035$ |
$6.932125642$ |
1.308040105 |
\( -122654 a - 842076 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -17 a - 101\) , \( -64 a - 436\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-17a-101\right){x}-64a-436$ |
12.1-a1 |
12.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{7} \cdot 3^{7} \) |
$2.44999$ |
$(-a+8), (-a-7), (-52a-357)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$13.44075155$ |
1.824835336 |
\( \frac{166195231}{69984} a + \frac{1139844827}{69984} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 2401258290 a - 18887000841\) , \( -1781930806827389 a + 14015705361500025\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2401258290a-18887000841\right){x}-1781930806827389a+14015705361500025$ |
12.1-b1 |
12.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{7} \cdot 3^{7} \) |
$2.44999$ |
$(-a+8), (-a-7), (-52a-357)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.078437573$ |
$11.87551769$ |
1.770536432 |
\( \frac{166195231}{69984} a + \frac{1139844827}{69984} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -269 a - 1827\) , \( 7022 a + 48214\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-269a-1827\right){x}+7022a+48214$ |
12.1-c1 |
12.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$2.44999$ |
$(-a+8), (-a-7), (-52a-357)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.419617984$ |
0.328508743 |
\( \frac{862466072125}{429981696} a - \frac{3261071985131}{214990848} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 5 a - 12\) , \( 8 a - 36\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-12\right){x}+8a-36$ |
12.1-c2 |
12.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{10} \cdot 3^{16} \) |
$2.44999$ |
$(-a+8), (-a-7), (-52a-357)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.419617984$ |
0.328508743 |
\( -\frac{658839190694584165}{11019960576} a + \frac{2591060113241350883}{5509980288} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 65 a - 512\) , \( 668 a - 5280\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(65a-512\right){x}+668a-5280$ |
12.1-d1 |
12.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{27} \cdot 3 \) |
$2.44999$ |
$(-a+8), (-a-7), (-52a-357)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$4.725924539$ |
3.849799944 |
\( \frac{36095551}{98304} a + \frac{247714811}{98304} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -97 a - 663\) , \( -1164 a - 8000\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-97a-663\right){x}-1164a-8000$ |
12.1-d2 |
12.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$2.44999$ |
$(-a+8), (-a-7), (-52a-357)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$4.725924539$ |
3.849799944 |
\( \frac{5784954706489}{864} a + \frac{39716374742807}{864} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -10256644 a + 80673218\) , \( -2022736447430 a + 15909752478878\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-10256644a+80673218\right){x}-2022736447430a+15909752478878$ |
12.1-e1 |
12.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{27} \cdot 3 \) |
$2.44999$ |
$(-a+8), (-a-7), (-52a-357)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.152598850$ |
$11.35308701$ |
2.822582225 |
\( \frac{36095551}{98304} a + \frac{247714811}{98304} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 15849071845 a - 124660239549\) , \( -122912772997547574 a + 966765491060639043\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(15849071845a-124660239549\right){x}-122912772997547574a+966765491060639043$ |
12.1-e2 |
12.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$2.44999$ |
$(-a+8), (-a-7), (-52a-357)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.457796550$ |
$11.35308701$ |
2.822582225 |
\( \frac{5784954706489}{864} a + \frac{39716374742807}{864} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -1275546 a - 8757206\) , \( 2127641751 a + 14607239178\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-1275546a-8757206\right){x}+2127641751a+14607239178$ |
12.1-f1 |
12.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{11} \cdot 3^{15} \) |
$2.44999$ |
$(-a+8), (-a-7), (-52a-357)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
$0.014587921$ |
$9.455028562$ |
7.865125872 |
\( \frac{1514638126999}{1836660096} a + \frac{5110717728563}{1836660096} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 315558654 a - 2482013931\) , \( -10476032628218 a + 82398814876539\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(315558654a-2482013931\right){x}-10476032628218a+82398814876539$ |
12.1-g1 |
12.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{217}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{11} \cdot 3^{15} \) |
$2.44999$ |
$(-a+8), (-a-7), (-52a-357)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$2.521591970$ |
4.792950870 |
\( \frac{1514638126999}{1836660096} a + \frac{5110717728563}{1836660096} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -345489 a - 2371916\) , \( -269827466 a - 1852489645\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-345489a-2371916\right){x}-269827466a-1852489645$ |
*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.