| 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 |
| 11.1-a1 |
11.1-a |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$10.51283$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$664.2737262$ |
1.904935554 |
\( \frac{15055093632}{1331} a^{3} - \frac{27625508544}{1331} a^{2} - \frac{84548939520}{1331} a + \frac{155282541184}{1331} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{3} + 4 a\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -5 a^{3} + 5 a^{2} + 25 a - 31\) , \( 5 a^{3} - 12 a^{2} - 30 a + 64\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-5a^{3}+5a^{2}+25a-31\right){x}+5a^{3}-12a^{2}-30a+64$ |
| 11.1-a2 |
11.1-a |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$10.51283$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$664.2737262$ |
1.904935554 |
\( -\frac{136304275584}{11} a^{3} + \frac{323073924672}{11} a^{2} + \frac{460976394240}{11} a - \frac{1092625073792}{11} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a\) , \( a\) , \( a^{3} - 4 a^{2} + 13\) , \( 3 a^{3} - 6 a^{2} - 10 a + 20\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(a^{3}-4a^{2}+13\right){x}+3a^{3}-6a^{2}-10a+20$ |
| 11.1-a3 |
11.1-a |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{6} \) |
$10.51283$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$332.1368631$ |
1.904935554 |
\( \frac{1800220800}{1771561} a^{3} - \frac{4662715072}{1771561} a^{2} - \frac{10261448064}{1771561} a + \frac{26528193856}{1771561} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a + 1\) , \( a + 1\) , \( 3 a^{3} + 6 a^{2} - 16 a - 30\) , \( 10 a^{3} + 18 a^{2} - 55 a - 100\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a^{3}+6a^{2}-16a-30\right){x}+10a^{3}+18a^{2}-55a-100$ |
| 11.1-a4 |
11.1-a |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$10.51283$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$332.1368631$ |
1.904935554 |
\( -\frac{1462185600}{121} a^{3} - \frac{2728280768}{121} a^{2} + \frac{8223840384}{121} a + \frac{15305693248}{121} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + 4 a - 1\) , \( a^{3} - 5 a\) , \( 4 a^{2} - 17\) , \( 12 a^{3} + 31 a^{2} - 40 a - 106\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a^{3}+4a-1\right){x}^{2}+\left(4a^{2}-17\right){x}+12a^{3}+31a^{2}-40a-106$ |
| 11.1-b1 |
11.1-b |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$10.51283$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.321689641$ |
$232.7714607$ |
1.717868866 |
\( -\frac{1462185600}{121} a^{3} - \frac{2728280768}{121} a^{2} + \frac{8223840384}{121} a + \frac{15305693248}{121} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} + a^{2} - 4 a - 5\) , \( 2 a^{3} + 4 a^{2} - 7 a - 13\) , \( 50 a^{3} + 117 a^{2} - 170 a - 397\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{3}+a^{2}-4a-5\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+4\right){x}^{2}+\left(2a^{3}+4a^{2}-7a-13\right){x}+50a^{3}+117a^{2}-170a-397$ |
| 11.1-b2 |
11.1-b |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$10.51283$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.214459761$ |
$232.7714607$ |
1.717868866 |
\( \frac{15055093632}{1331} a^{3} - \frac{27625508544}{1331} a^{2} - \frac{84548939520}{1331} a + \frac{155282541184}{1331} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( -a^{3} - a^{2} + 6 a + 5\) , \( a^{3} - 5 a + 1\) , \( -6 a^{3} - 5 a^{2} + 32 a + 23\) , \( -7 a^{3} - 8 a^{2} + 36 a + 37\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a+5\right){x}^{2}+\left(-6a^{3}-5a^{2}+32a+23\right){x}-7a^{3}-8a^{2}+36a+37$ |
| 11.1-b3 |
11.1-b |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{6} \) |
$10.51283$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.107229880$ |
$232.7714607$ |
1.717868866 |
\( \frac{1800220800}{1771561} a^{3} - \frac{4662715072}{1771561} a^{2} - \frac{10261448064}{1771561} a + \frac{26528193856}{1771561} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 6\) , \( a^{3} + a^{2} - 4 a - 5\) , \( 3 a^{3} + 6 a^{2} - 13 a - 25\) , \( a^{3} + a + 8\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-5\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-6\right){x}^{2}+\left(3a^{3}+6a^{2}-13a-25\right){x}+a^{3}+a+8$ |
| 11.1-b4 |
11.1-b |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$10.51283$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.643379283$ |
$232.7714607$ |
1.717868866 |
\( -\frac{136304275584}{11} a^{3} + \frac{323073924672}{11} a^{2} + \frac{460976394240}{11} a - \frac{1092625073792}{11} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 4\) , \( 9 a^{3} - 9 a^{2} - 31 a + 29\) , \( 21 a^{3} - 32 a^{2} - 71 a + 106\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(9a^{3}-9a^{2}-31a+29\right){x}+21a^{3}-32a^{2}-71a+106$ |
| 11.2-a1 |
11.2-a |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( -11 \) |
$10.51283$ |
$(a^3-a^2-5a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$664.2737262$ |
1.904935554 |
\( \frac{136304275584}{11} a^{3} + \frac{323073924672}{11} a^{2} - \frac{460976394240}{11} a - \frac{1092625073792}{11} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{2} - 5\) , \( -15 a^{3} - 38 a^{2} + 50 a + 133\) , \( -108 a^{3} - 258 a^{2} + 364 a + 874\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(-15a^{3}-38a^{2}+50a+133\right){x}-108a^{3}-258a^{2}+364a+874$ |
| 11.2-a2 |
11.2-a |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{3} \) |
$10.51283$ |
$(a^3-a^2-5a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$664.2737262$ |
1.904935554 |
\( -\frac{15055093632}{1331} a^{3} - \frac{27625508544}{1331} a^{2} + \frac{84548939520}{1331} a + \frac{155282541184}{1331} \) |
\( \bigl[a^{2} + a - 5\) , \( a\) , \( a^{3} + a^{2} - 4 a - 4\) , \( 4 a^{3} + 5 a^{2} - 22 a - 31\) , \( -6 a^{3} - 12 a^{2} + 33 a + 64\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+a{x}^{2}+\left(4a^{3}+5a^{2}-22a-31\right){x}-6a^{3}-12a^{2}+33a+64$ |
| 11.2-a3 |
11.2-a |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{6} \) |
$10.51283$ |
$(a^3-a^2-5a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$332.1368631$ |
1.904935554 |
\( -\frac{1800220800}{1771561} a^{3} - \frac{4662715072}{1771561} a^{2} + \frac{10261448064}{1771561} a + \frac{26528193856}{1771561} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a + 1\) , \( a^{3} - 5 a\) , \( -5 a^{3} + 10 a^{2} + 30 a - 51\) , \( -2 a^{3} + 4 a^{2} + 13 a - 19\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a^{3}+10a^{2}+30a-51\right){x}-2a^{3}+4a^{2}+13a-19$ |
| 11.2-a4 |
11.2-a |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$10.51283$ |
$(a^3-a^2-5a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$332.1368631$ |
1.904935554 |
\( \frac{1462185600}{121} a^{3} - \frac{2728280768}{121} a^{2} - \frac{8223840384}{121} a + \frac{15305693248}{121} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -1\) , \( a^{3} - 5 a\) , \( -a^{3} + 4 a^{2} + 5 a - 17\) , \( -12 a^{3} + 31 a^{2} + 40 a - 106\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}-{x}^{2}+\left(-a^{3}+4a^{2}+5a-17\right){x}-12a^{3}+31a^{2}+40a-106$ |
| 11.2-b1 |
11.2-b |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$10.51283$ |
$(a^3-a^2-5a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.321689641$ |
$232.7714607$ |
1.717868866 |
\( \frac{1462185600}{121} a^{3} - \frac{2728280768}{121} a^{2} - \frac{8223840384}{121} a + \frac{15305693248}{121} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{2} - 5\) , \( a^{2} - 4\) , \( -a^{3} + 3 a^{2} + 5 a - 15\) , \( -4 a^{3} + 9 a^{2} + 16 a - 35\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-a^{3}+3a^{2}+5a-15\right){x}-4a^{3}+9a^{2}+16a-35$ |
| 11.2-b2 |
11.2-b |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{3} \) |
$10.51283$ |
$(a^3-a^2-5a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.214459761$ |
$232.7714607$ |
1.717868866 |
\( -\frac{15055093632}{1331} a^{3} - \frac{27625508544}{1331} a^{2} + \frac{84548939520}{1331} a + \frac{155282541184}{1331} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - a^{2} - 4 a + 5\) , \( a\) , \( 2 a^{3} - 10 a + 2\) , \( 4 a^{3} + 6 a^{2} - 22 a - 34\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-4a+5\right){x}^{2}+\left(2a^{3}-10a+2\right){x}+4a^{3}+6a^{2}-22a-34$ |
| 11.2-b3 |
11.2-b |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{6} \) |
$10.51283$ |
$(a^3-a^2-5a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.107229880$ |
$232.7714607$ |
1.717868866 |
\( -\frac{1800220800}{1771561} a^{3} - \frac{4662715072}{1771561} a^{2} + \frac{10261448064}{1771561} a + \frac{26528193856}{1771561} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 6\) , \( a^{2} - 4\) , \( 9 a^{2} + 5 a - 35\) , \( 4 a^{3} + 7 a^{2} - 15 a - 23\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-6\right){x}^{2}+\left(9a^{2}+5a-35\right){x}+4a^{3}+7a^{2}-15a-23$ |
| 11.2-b4 |
11.2-b |
$4$ |
$6$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( -11 \) |
$10.51283$ |
$(a^3-a^2-5a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.643379283$ |
$232.7714607$ |
1.717868866 |
\( \frac{136304275584}{11} a^{3} + \frac{323073924672}{11} a^{2} - \frac{460976394240}{11} a - \frac{1092625073792}{11} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{2} - 5\) , \( -2 a^{3} - 6 a^{2} + 5 a + 20\) , \( -37 a^{3} - 86 a^{2} + 126 a + 289\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(-2a^{3}-6a^{2}+5a+20\right){x}-37a^{3}-86a^{2}+126a+289$ |
| 16.1-a1 |
16.1-a |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$797.0884668$ |
1.714355958 |
\( 12327033619260 a^{3} + 29218018687500 a^{2} - 41689608540720 a - 98814345780100 \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + 6\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 11 a^{3} + 14 a^{2} - 61 a - 86\) , \( -31 a^{3} - 44 a^{2} + 172 a + 250\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(11a^{3}+14a^{2}-61a-86\right){x}-31a^{3}-44a^{2}+172a+250$ |
| 16.1-a2 |
16.1-a |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$797.0884668$ |
1.714355958 |
\( -12327033619260 a^{3} + 29218018687500 a^{2} + 41689608540720 a - 98814345780100 \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{3} - a^{2} + 5 a + 6\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -11 a^{3} + 14 a^{2} + 59 a - 86\) , \( 31 a^{3} - 44 a^{2} - 173 a + 250\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+6\right){x}^{2}+\left(-11a^{3}+14a^{2}+59a-86\right){x}+31a^{3}-44a^{2}-173a+250$ |
| 16.1-a3 |
16.1-a |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$199.2721167$ |
1.714355958 |
\( -202240 a^{3} + 480000 a^{2} + 686080 a - 1625600 \) |
\( \bigl[0\) , \( a^{3} - 6 a\) , \( 0\) , \( -6 a^{3} - 17 a^{2} + 22 a + 68\) , \( 15 a^{3} + 33 a^{2} - 55 a - 116\bigr] \) |
${y}^2={x}^{3}+\left(a^{3}-6a\right){x}^{2}+\left(-6a^{3}-17a^{2}+22a+68\right){x}+15a^{3}+33a^{2}-55a-116$ |
| 16.1-a4 |
16.1-a |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$199.2721167$ |
1.714355958 |
\( 202240 a^{3} + 480000 a^{2} - 686080 a - 1625600 \) |
\( \bigl[0\) , \( -a^{3} + 6 a\) , \( 0\) , \( 6 a^{3} - 17 a^{2} - 22 a + 68\) , \( -15 a^{3} + 33 a^{2} + 55 a - 116\bigr] \) |
${y}^2={x}^{3}+\left(-a^{3}+6a\right){x}^{2}+\left(6a^{3}-17a^{2}-22a+68\right){x}-15a^{3}+33a^{2}+55a-116$ |
| 16.1-a5 |
16.1-a |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 3 \) |
$1$ |
$49.81802918$ |
1.714355958 |
\( 268422012747460 a^{3} - 493631366431500 a^{2} - 1508003990944720 a + 2773237794524500 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -4 a^{3} + 16 a^{2} + 17 a - 70\) , \( -3 a^{3} + 16 a^{2} + 20 a - 90\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+{x}^{2}+\left(-4a^{3}+16a^{2}+17a-70\right){x}-3a^{3}+16a^{2}+20a-90$ |
| 16.1-a6 |
16.1-a |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 3 \) |
$1$ |
$797.0884668$ |
1.714355958 |
\( 6791040 a^{3} - 7950000 a^{2} - 35741280 a + 50380400 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 3 a - 5\) , \( 2 a^{3} - 7 a - 3\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+{x}^{2}+\left(a^{3}+a^{2}-3a-5\right){x}+2a^{3}-7a-3$ |
| 16.1-a7 |
16.1-a |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 3 \) |
$1$ |
$49.81802918$ |
1.714355958 |
\( -268422012747460 a^{3} - 493631366431500 a^{2} + 1508003990944720 a + 2773237794524500 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 2 a^{3} + 16 a^{2} - 9 a - 70\) , \( 3 a^{3} + 16 a^{2} - 21 a - 90\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(2a^{3}+16a^{2}-9a-70\right){x}+3a^{3}+16a^{2}-21a-90$ |
| 16.1-a8 |
16.1-a |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 3 \) |
$1$ |
$797.0884668$ |
1.714355958 |
\( -6791040 a^{3} - 7950000 a^{2} + 35741280 a + 50380400 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -3 a^{3} + a^{2} + 11 a - 5\) , \( -2 a^{3} + 6 a - 3\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-3a^{3}+a^{2}+11a-5\right){x}-2a^{3}+6a-3$ |
| 16.1-b1 |
16.1-b |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$525.0606260$ |
1.505714610 |
\( 268422012747460 a^{3} - 493631366431500 a^{2} - 1508003990944720 a + 2773237794524500 \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} + a - 4\) , \( a^{2} + a - 5\) , \( -8 a^{3} + 22 a^{2} + 30 a - 83\) , \( 16 a^{3} - 37 a^{2} - 55 a + 128\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-8a^{3}+22a^{2}+30a-83\right){x}+16a^{3}-37a^{2}-55a+128$ |
| 16.1-b2 |
16.1-b |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$525.0606260$ |
1.505714610 |
\( -268422012747460 a^{3} - 493631366431500 a^{2} + 1508003990944720 a + 2773237794524500 \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( a^{2} + a - 5\) , \( 6 a^{3} + 22 a^{2} - 20 a - 83\) , \( -17 a^{3} - 37 a^{2} + 60 a + 128\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-4\right){x}^{2}+\left(6a^{3}+22a^{2}-20a-83\right){x}-17a^{3}-37a^{2}+60a+128$ |
| 16.1-b3 |
16.1-b |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$525.0606260$ |
1.505714610 |
\( -12327033619260 a^{3} + 29218018687500 a^{2} + 41689608540720 a - 98814345780100 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( -a\) , \( a^{2} + a - 5\) , \( -5 a^{3} - 2 a^{2} + 23 a - 7\) , \( -9 a^{3} + 35 a^{2} + 60 a - 172\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}-a{x}^{2}+\left(-5a^{3}-2a^{2}+23a-7\right){x}-9a^{3}+35a^{2}+60a-172$ |
| 16.1-b4 |
16.1-b |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$2100.242504$ |
1.505714610 |
\( -6791040 a^{3} - 7950000 a^{2} + 35741280 a + 50380400 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( -a\) , \( a^{2} + a - 5\) , \( -2 a^{2} - 2 a + 8\) , \( -a^{3} + 5 a - 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}-a{x}^{2}+\left(-2a^{2}-2a+8\right){x}-a^{3}+5a-2$ |
| 16.1-b5 |
16.1-b |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$525.0606260$ |
1.505714610 |
\( 12327033619260 a^{3} + 29218018687500 a^{2} - 41689608540720 a - 98814345780100 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( 0\) , \( a^{2} + a - 5\) , \( 5 a^{3} - 2 a^{2} - 25 a - 7\) , \( 8 a^{3} + 35 a^{2} - 55 a - 172\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(5a^{3}-2a^{2}-25a-7\right){x}+8a^{3}+35a^{2}-55a-172$ |
| 16.1-b6 |
16.1-b |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$2100.242504$ |
1.505714610 |
\( 6791040 a^{3} - 7950000 a^{2} - 35741280 a + 50380400 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( 0\) , \( a^{2} + a - 5\) , \( -2 a^{2} + 8\) , \( -2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-2a^{2}+8\right){x}-2$ |
| 16.1-b7 |
16.1-b |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$525.0606260$ |
1.505714610 |
\( 202240 a^{3} + 480000 a^{2} - 686080 a - 1625600 \) |
\( \bigl[0\) , \( -a^{3} + 4 a\) , \( 0\) , \( 4 a^{3} - 6 a^{2} - 18 a + 28\) , \( -2 a^{3} + 3 a^{2} + 10 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(4a^{3}-6a^{2}-18a+28\right){x}-2a^{3}+3a^{2}+10a-16$ |
| 16.1-b8 |
16.1-b |
$8$ |
$12$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$11.01692$ |
$(a^3-a^2-5a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$525.0606260$ |
1.505714610 |
\( -202240 a^{3} + 480000 a^{2} + 686080 a - 1625600 \) |
\( \bigl[0\) , \( -a^{3} + 5 a\) , \( 0\) , \( -14 a^{3} - 34 a^{2} + 48 a + 119\) , \( 55 a^{3} + 131 a^{2} - 185 a - 442\bigr] \) |
${y}^2={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-14a^{3}-34a^{2}+48a+119\right){x}+55a^{3}+131a^{2}-185a-442$ |
| 19.2-a1 |
19.2-a |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$11.25614$ |
$(-a^2-a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$185.1232086$ |
2.123508838 |
\( \frac{664654622}{6859} a^{3} - \frac{1594111146}{6859} a^{2} - \frac{114593609}{361} a + \frac{276991685}{361} \) |
\( \bigl[a^{3} - 5 a\) , \( a^{3} - a^{2} - 6 a + 6\) , \( 0\) , \( 3 a^{3} - 10 a^{2} - 16 a + 54\) , \( a^{3} - 16 a^{2} - 4 a + 86\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-6a+6\right){x}^{2}+\left(3a^{3}-10a^{2}-16a+54\right){x}+a^{3}-16a^{2}-4a+86$ |
| 19.2-a2 |
19.2-a |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$11.25614$ |
$(-a^2-a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$185.1232086$ |
2.123508838 |
\( -\frac{1826162069}{19} a^{3} - \frac{4329320481}{19} a^{2} + 324861206 a + 770258954 \) |
\( \bigl[a^{3} - 5 a + 1\) , \( a^{3} - a^{2} - 5 a + 4\) , \( a^{3} - 4 a + 1\) , \( 26 a^{3} - 50 a^{2} - 148 a + 280\) , \( 128 a^{3} - 238 a^{2} - 719 a + 1331\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+4\right){x}^{2}+\left(26a^{3}-50a^{2}-148a+280\right){x}+128a^{3}-238a^{2}-719a+1331$ |
| 19.2-b1 |
19.2-b |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{9} \) |
$11.25614$ |
$(-a^2-a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$145.9225457$ |
1.673846396 |
\( -\frac{25171096360259318}{322687697779} a^{3} - \frac{57335570600443566}{322687697779} a^{2} + \frac{4536787697604377}{16983563041} a + \frac{10092211830823702}{16983563041} \) |
\( \bigl[a^{3} - 5 a\) , \( -a^{3} + 6 a - 1\) , \( a^{3} - 5 a\) , \( -41 a^{3} + 69 a^{2} + 228 a - 390\) , \( 333 a^{3} - 613 a^{2} - 1869 a + 3445\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a^{3}+6a-1\right){x}^{2}+\left(-41a^{3}+69a^{2}+228a-390\right){x}+333a^{3}-613a^{2}-1869a+3445$ |
| 19.2-b2 |
19.2-b |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$11.25614$ |
$(-a^2-a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$145.9225457$ |
1.673846396 |
\( -\frac{2056216931647933}{6859} a^{3} + \frac{3786239627381886}{6859} a^{2} + \frac{607994558845765}{361} a - \frac{1119538049134760}{361} \) |
\( \bigl[1\) , \( a^{3} - 4 a + 1\) , \( a^{2} - 5\) , \( 45 a^{3} - 104 a^{2} - 142 a + 330\) , \( -527 a^{3} + 1258 a^{2} + 1761 a - 4219\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(45a^{3}-104a^{2}-142a+330\right){x}-527a^{3}+1258a^{2}+1761a-4219$ |
| 19.2-c1 |
19.2-c |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{9} \) |
$11.25614$ |
$(-a^2-a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$108.3017008$ |
1.242305708 |
\( -\frac{25171096360259318}{322687697779} a^{3} - \frac{57335570600443566}{322687697779} a^{2} + \frac{4536787697604377}{16983563041} a + \frac{10092211830823702}{16983563041} \) |
\( \bigl[a^{2} - 5\) , \( -a^{3} + a^{2} + 4 a - 6\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -102 a^{3} + 189 a^{2} + 572 a - 1058\) , \( -1109 a^{3} + 2038 a^{2} + 6229 a - 11451\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-6\right){x}^{2}+\left(-102a^{3}+189a^{2}+572a-1058\right){x}-1109a^{3}+2038a^{2}+6229a-11451$ |
| 19.2-c2 |
19.2-c |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$11.25614$ |
$(-a^2-a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$108.3017008$ |
1.242305708 |
\( -\frac{2056216931647933}{6859} a^{3} + \frac{3786239627381886}{6859} a^{2} + \frac{607994558845765}{361} a - \frac{1119538049134760}{361} \) |
\( \bigl[a^{3} - 5 a\) , \( -a^{2} + a + 4\) , \( a^{3} - 5 a\) , \( 5 a^{3} - 16 a^{2} + 13 a - 8\) , \( -199 a^{3} + 440 a^{2} + 809 a - 1740\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(5a^{3}-16a^{2}+13a-8\right){x}-199a^{3}+440a^{2}+809a-1740$ |
| 19.2-d1 |
19.2-d |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$11.25614$ |
$(-a^2-a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$38.55616366$ |
0.442269529 |
\( \frac{664654622}{6859} a^{3} - \frac{1594111146}{6859} a^{2} - \frac{114593609}{361} a + \frac{276991685}{361} \) |
\( \bigl[a^{2} - 5\) , \( a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - 4 a + 1\) , \( -2 a^{3} - 4 a^{2} + 13 a + 27\) , \( 17 a^{3} + 31 a^{2} - 95 a - 175\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-4\right){x}^{2}+\left(-2a^{3}-4a^{2}+13a+27\right){x}+17a^{3}+31a^{2}-95a-175$ |
| 19.2-d2 |
19.2-d |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$11.25614$ |
$(-a^2-a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$38.55616366$ |
0.442269529 |
\( -\frac{1826162069}{19} a^{3} - \frac{4329320481}{19} a^{2} + 324861206 a + 770258954 \) |
\( \bigl[a + 1\) , \( a\) , \( a^{3} - 5 a\) , \( 9 a^{3} - 18 a^{2} - 50 a + 106\) , \( -19 a^{3} + 36 a^{2} + 110 a - 206\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+a{x}^{2}+\left(9a^{3}-18a^{2}-50a+106\right){x}-19a^{3}+36a^{2}+110a-206$ |
| 19.3-a1 |
19.3-a |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19 \) |
$11.25614$ |
$(a^2-a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$185.1232086$ |
2.123508838 |
\( \frac{1826162069}{19} a^{3} - \frac{4329320481}{19} a^{2} - 324861206 a + 770258954 \) |
\( \bigl[a^{2} + a - 4\) , \( a^{3} + a^{2} - 4 a - 5\) , \( a^{3} - 5 a + 1\) , \( -a^{3} - 2 a^{2} + 11 a + 26\) , \( 2 a^{2} + 2 a - 7\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-5\right){x}^{2}+\left(-a^{3}-2a^{2}+11a+26\right){x}+2a^{2}+2a-7$ |
| 19.3-a2 |
19.3-a |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19^{3} \) |
$11.25614$ |
$(a^2-a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$185.1232086$ |
2.123508838 |
\( -\frac{664654622}{6859} a^{3} - \frac{1594111146}{6859} a^{2} + \frac{114593609}{361} a + \frac{276991685}{361} \) |
\( \bigl[a^{3} - 5 a\) , \( -a^{3} - a^{2} + 6 a + 6\) , \( 0\) , \( -3 a^{3} - 10 a^{2} + 16 a + 54\) , \( -a^{3} - 16 a^{2} + 4 a + 86\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}={x}^{3}+\left(-a^{3}-a^{2}+6a+6\right){x}^{2}+\left(-3a^{3}-10a^{2}+16a+54\right){x}-a^{3}-16a^{2}+4a+86$ |
| 19.3-b1 |
19.3-b |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19^{3} \) |
$11.25614$ |
$(a^2-a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$145.9225457$ |
1.673846396 |
\( \frac{2056216931647933}{6859} a^{3} + \frac{3786239627381886}{6859} a^{2} - \frac{607994558845765}{361} a - \frac{1119538049134760}{361} \) |
\( \bigl[a^{2} - 4\) , \( a^{3} + a^{2} - 5 a - 6\) , \( a^{3} - 5 a + 1\) , \( -336 a^{3} - 796 a^{2} + 1137 a + 2694\) , \( 8684 a^{3} + 20586 a^{2} - 29365 a - 69618\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-6\right){x}^{2}+\left(-336a^{3}-796a^{2}+1137a+2694\right){x}+8684a^{3}+20586a^{2}-29365a-69618$ |
| 19.3-b2 |
19.3-b |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19^{9} \) |
$11.25614$ |
$(a^2-a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$145.9225457$ |
1.673846396 |
\( \frac{25171096360259318}{322687697779} a^{3} - \frac{57335570600443566}{322687697779} a^{2} - \frac{4536787697604377}{16983563041} a + \frac{10092211830823702}{16983563041} \) |
\( \bigl[a^{3} - 5 a\) , \( a^{3} - 6 a - 1\) , \( a^{3} - 5 a\) , \( 41 a^{3} + 69 a^{2} - 228 a - 390\) , \( -333 a^{3} - 613 a^{2} + 1869 a + 3445\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(a^{3}-6a-1\right){x}^{2}+\left(41a^{3}+69a^{2}-228a-390\right){x}-333a^{3}-613a^{2}+1869a+3445$ |
| 19.3-c1 |
19.3-c |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19^{3} \) |
$11.25614$ |
$(a^2-a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$108.3017008$ |
1.242305708 |
\( \frac{2056216931647933}{6859} a^{3} + \frac{3786239627381886}{6859} a^{2} - \frac{607994558845765}{361} a - \frac{1119538049134760}{361} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 6 a - 5\) , \( a^{2} + a - 4\) , \( -126 a^{3} - 303 a^{2} + 421 a + 1022\) , \( 1976 a^{3} + 4683 a^{2} - 6694 a - 15863\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-5\right){x}^{2}+\left(-126a^{3}-303a^{2}+421a+1022\right){x}+1976a^{3}+4683a^{2}-6694a-15863$ |
| 19.3-c2 |
19.3-c |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19^{9} \) |
$11.25614$ |
$(a^2-a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$108.3017008$ |
1.242305708 |
\( \frac{25171096360259318}{322687697779} a^{3} - \frac{57335570600443566}{322687697779} a^{2} - \frac{4536787697604377}{16983563041} a + \frac{10092211830823702}{16983563041} \) |
\( \bigl[1\) , \( -a^{3} + 5 a - 1\) , \( a^{2} - 4\) , \( 18 a^{3} + 24 a^{2} - 95 a - 139\) , \( 75 a^{3} + 148 a^{2} - 429 a - 825\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{3}+5a-1\right){x}^{2}+\left(18a^{3}+24a^{2}-95a-139\right){x}+75a^{3}+148a^{2}-429a-825$ |
| 19.3-d1 |
19.3-d |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19^{3} \) |
$11.25614$ |
$(a^2-a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$38.55616366$ |
0.442269529 |
\( -\frac{664654622}{6859} a^{3} - \frac{1594111146}{6859} a^{2} + \frac{114593609}{361} a + \frac{276991685}{361} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 5 a + 5\) , \( a^{2} - 5\) , \( -6 a^{2} - 3 a + 27\) , \( -2 a^{3} - 6 a^{2} + 6 a + 21\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+5\right){x}^{2}+\left(-6a^{2}-3a+27\right){x}-2a^{3}-6a^{2}+6a+21$ |
| 19.3-d2 |
19.3-d |
$2$ |
$3$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19 \) |
$11.25614$ |
$(a^2-a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$38.55616366$ |
0.442269529 |
\( \frac{1826162069}{19} a^{3} - \frac{4329320481}{19} a^{2} - 324861206 a + 770258954 \) |
\( \bigl[a + 1\) , \( a\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -10 a^{3} - 19 a^{2} + 57 a + 108\) , \( 2 a^{3} + 3 a^{2} - 12 a - 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+a{x}^{2}+\left(-10a^{3}-19a^{2}+57a+108\right){x}+2a^{3}+3a^{2}-12a-20$ |
| 29.1-a1 |
29.1-a |
$1$ |
$1$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$11.86711$ |
$(-2a^2+a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.053953137$ |
$492.8277444$ |
2.440029340 |
\( \frac{628685}{841} a^{3} + \frac{808824}{841} a^{2} - \frac{3101693}{841} a - \frac{4531767}{841} \) |
\( \bigl[1\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{2} + a - 4\) , \( 15 a^{3} + 36 a^{2} - 51 a - 121\) , \( -70 a^{3} - 165 a^{2} + 237 a + 557\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+4\right){x}^{2}+\left(15a^{3}+36a^{2}-51a-121\right){x}-70a^{3}-165a^{2}+237a+557$ |
| 29.1-b1 |
29.1-b |
$1$ |
$1$ |
4.4.7600.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$11.86711$ |
$(-2a^2+a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.046354480$ |
$736.4654095$ |
3.132761006 |
\( \frac{628685}{841} a^{3} + \frac{808824}{841} a^{2} - \frac{3101693}{841} a - \frac{4531767}{841} \) |
\( \bigl[a^{3} - 5 a\) , \( a^{2} - a - 4\) , \( a^{2} - 5\) , \( 6 a^{3} + 14 a^{2} - 23 a - 46\) , \( -11 a^{3} - 25 a^{2} + 37 a + 85\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(6a^{3}+14a^{2}-23a-46\right){x}-11a^{3}-25a^{2}+37a+85$ |
*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.
