| 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 |
| 1.1-a1 |
1.1-a |
$6$ |
$50$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.99626$ |
$\textsf{none}$ |
$0$ |
$\Z/10\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$5$ |
5Cs.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1512.581761$ |
0.338223563 |
\( 1728 \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{2} + a - 2\) , \( -a^{3} - 2 a^{2} + 3 a + 5\) , \( -a - 1\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(-a^{3}-2a^{2}+3a+5\right){x}-a-1$ |
| 1.1-a2 |
1.1-a |
$6$ |
$50$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.99626$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-100$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$5$ |
5B.1.4[2] |
$25$ |
\( 1 \) |
$1$ |
$2.420130817$ |
0.338223563 |
\( 19691491018752 a^{2} - 27212977933632 \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{2} + a - 2\) , \( 119 a^{3} - 152 a^{2} - 217 a + 135\) , \( 1098 a^{3} - 1803 a^{2} - 1718 a + 2224\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(119a^{3}-152a^{2}-217a+135\right){x}+1098a^{3}-1803a^{2}-1718a+2224$ |
| 1.1-a3 |
1.1-a |
$6$ |
$50$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.99626$ |
$\textsf{none}$ |
$0$ |
$\Z/10\Z$ |
$\textsf{potential}$ |
$-100$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$5$ |
5B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1512.581761$ |
0.338223563 |
\( 19691491018752 a^{2} - 27212977933632 \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{2} + a - 2\) , \( 119 a^{3} - 152 a^{2} - 217 a + 135\) , \( -1268 a^{3} + 1963 a^{2} + 2076 a - 2326\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(119a^{3}-152a^{2}-217a+135\right){x}-1268a^{3}+1963a^{2}+2076a-2326$ |
| 1.1-a4 |
1.1-a |
$6$ |
$50$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.99626$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-100$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$5$ |
5B.1.4[2] |
$25$ |
\( 1 \) |
$1$ |
$2.420130817$ |
0.338223563 |
\( -19691491018752 a^{2} + 71244477160128 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( 140 a^{3} + 150 a^{2} - 541 a - 619\) , \( 1727 a^{3} + 1963 a^{2} - 6449 a - 7491\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(140a^{3}+150a^{2}-541a-619\right){x}+1727a^{3}+1963a^{2}-6449a-7491$ |
| 1.1-a5 |
1.1-a |
$6$ |
$50$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.99626$ |
$\textsf{none}$ |
$0$ |
$\Z/10\Z$ |
$\textsf{potential}$ |
$-100$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$5$ |
5B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1512.581761$ |
0.338223563 |
\( -19691491018752 a^{2} + 71244477160128 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( 140 a^{3} + 150 a^{2} - 541 a - 619\) , \( -1577 a^{3} - 1803 a^{2} + 5829 a + 6789\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(140a^{3}+150a^{2}-541a-619\right){x}-1577a^{3}-1803a^{2}+5829a+6789$ |
| 1.1-a6 |
1.1-a |
$6$ |
$50$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.99626$ |
$\textsf{none}$ |
$0$ |
$\Z/10\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$5$ |
5Cs.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1512.581761$ |
0.338223563 |
\( 1728 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( -a + 1\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}-1$ |
| 25.1-a1 |
25.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$5.97580$ |
$(a)$ |
$0$ |
$\Z/10\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$2086.205928$ |
0.932979654 |
\( 565760 a^{2} - 782400 \) |
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{2} + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -6 a^{3} + 6 a^{2} + 22 a - 24\) , \( 25 a^{3} - 28 a^{2} - 91 a + 102\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-6a^{3}+6a^{2}+22a-24\right){x}+25a^{3}-28a^{2}-91a+102$ |
| 25.1-a2 |
25.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$5.97580$ |
$(a)$ |
$0$ |
$\Z/10\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$2086.205928$ |
0.932979654 |
\( -565760 a^{2} + 2046400 \) |
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{2} + a - 2\) , \( -5 a^{3} - 9 a^{2} + 8 a + 13\) , \( 15 a^{3} + 28 a^{2} - 21 a - 38\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(-5a^{3}-9a^{2}+8a+13\right){x}+15a^{3}+28a^{2}-21a-38$ |
| 25.1-a3 |
25.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$5.97580$ |
$(a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$83.44823715$ |
0.932979654 |
\( 565760 a^{2} - 782400 \) |
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{2} + 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 6 a^{3} + 6 a^{2} - 22 a - 23\) , \( 31 a^{3} + 36 a^{2} - 113 a - 132\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(6a^{3}+6a^{2}-22a-23\right){x}+31a^{3}+36a^{2}-113a-132$ |
| 25.1-a4 |
25.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$5.97580$ |
$(a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-20$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$83.44823715$ |
0.932979654 |
\( -565760 a^{2} + 2046400 \) |
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{2} + a - 2\) , \( 3 a^{3} - 9 a^{2} - 4 a + 14\) , \( 19 a^{3} - 36 a^{2} - 27 a + 48\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(3a^{3}-9a^{2}-4a+14\right){x}+19a^{3}-36a^{2}-27a+48$ |
| 59.1-a1 |
59.1-a |
$1$ |
$1$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{3} \) |
$6.65289$ |
$(a^3-a^2-2a+4)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1$ |
$67.12316258$ |
1.500919544 |
\( -\frac{7276684815}{205379} a^{3} + \frac{7434481239}{205379} a^{2} + \frac{25389289053}{205379} a - \frac{28299397059}{205379} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{2} - 2\) , \( -a^{3} + 4 a + 3\) , \( 5 a^{3} + 6 a^{2} - 18 a - 22\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-a^{3}+4a+3\right){x}+5a^{3}+6a^{2}-18a-22$ |
| 59.1-b1 |
59.1-b |
$1$ |
$1$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{3} \) |
$6.65289$ |
$(a^3-a^2-2a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3 \) |
$0.003152340$ |
$1465.929300$ |
1.239973629 |
\( -\frac{7276684815}{205379} a^{3} + \frac{7434481239}{205379} a^{2} + \frac{25389289053}{205379} a - \frac{28299397059}{205379} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a + 1\) , \( -a^{3} - 2 a^{2} + 3 a + 6\) , \( -4 a^{3} - 5 a^{2} + 14 a + 17\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-a^{3}-2a^{2}+3a+6\right){x}-4a^{3}-5a^{2}+14a+17$ |
| 59.2-a1 |
59.2-a |
$1$ |
$1$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( - 59^{3} \) |
$6.65289$ |
$(-a^3+a^2+4a-1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1$ |
$67.12316258$ |
1.500919544 |
\( -\frac{3559234608}{205379} a^{3} - \frac{7434481239}{205379} a^{2} + \frac{3401019009}{205379} a + \frac{8873009136}{205379} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + 2 a^{2} - 2 a - 3\) , \( 4 a^{3} - 3 a^{2} - 7 a + 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a^{3}+2a^{2}-2a-3\right){x}+4a^{3}-3a^{2}-7a+2$ |
| 59.2-b1 |
59.2-b |
$1$ |
$1$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( - 59^{3} \) |
$6.65289$ |
$(-a^3+a^2+4a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3 \) |
$0.003152340$ |
$1465.929300$ |
1.239973629 |
\( -\frac{3559234608}{205379} a^{3} - \frac{7434481239}{205379} a^{2} + \frac{3401019009}{205379} a + \frac{8873009136}{205379} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{3} - 3 a + 1\) , \( -a^{3} + 2 a + 1\) , \( -3 a^{3} + 5 a^{2} + 5 a - 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-a^{3}+2a+1\right){x}-3a^{3}+5a^{2}+5a-8$ |
| 59.3-a1 |
59.3-a |
$1$ |
$1$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
59.3 |
\( 59 \) |
\( - 59^{3} \) |
$6.65289$ |
$(a^3+a^2-4a-1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1$ |
$67.12316258$ |
1.500919544 |
\( \frac{3559234608}{205379} a^{3} - \frac{7434481239}{205379} a^{2} - \frac{3401019009}{205379} a + \frac{8873009136}{205379} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( a + 1\) , \( 1\) , \( 2 a^{2} + 3 a - 1\) , \( -2 a^{3} - 3 a^{2} + 4 a + 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-3\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a^{2}+3a-1\right){x}-2a^{3}-3a^{2}+4a+4$ |
| 59.3-b1 |
59.3-b |
$1$ |
$1$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
59.3 |
\( 59 \) |
\( - 59^{3} \) |
$6.65289$ |
$(a^3+a^2-4a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3 \) |
$0.003152340$ |
$1465.929300$ |
1.239973629 |
\( \frac{3559234608}{205379} a^{3} - \frac{7434481239}{205379} a^{2} - \frac{3401019009}{205379} a + \frac{8873009136}{205379} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{3} + a^{2} - 2 a - 3\) , \( -2 a^{3} - a^{2} + 6 a + 3\) , \( 3 a^{3} + 4 a^{2} - 5 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-2a^{3}-a^{2}+6a+3\right){x}+3a^{3}+4a^{2}-5a-5$ |
| 59.4-a1 |
59.4-a |
$1$ |
$1$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
59.4 |
\( 59 \) |
\( - 59^{3} \) |
$6.65289$ |
$(a^3+a^2-2a-4)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1$ |
$67.12316258$ |
1.500919544 |
\( \frac{7276684815}{205379} a^{3} + \frac{7434481239}{205379} a^{2} - \frac{25389289053}{205379} a - \frac{28299397059}{205379} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a\) , \( -a^{2} + 2 a + 5\) , \( -3 a^{3} + 6 a^{2} + 13 a - 21\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-a^{2}+2a+5\right){x}-3a^{3}+6a^{2}+13a-21$ |
| 59.4-b1 |
59.4-b |
$1$ |
$1$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
59.4 |
\( 59 \) |
\( - 59^{3} \) |
$6.65289$ |
$(a^3+a^2-2a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3 \) |
$0.003152340$ |
$1465.929300$ |
1.239973629 |
\( \frac{7276684815}{205379} a^{3} + \frac{7434481239}{205379} a^{2} - \frac{25389289053}{205379} a - \frac{28299397059}{205379} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -2 a^{2} + 5\) , \( 4 a^{3} - 6 a^{2} - 16 a + 20\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-2a^{2}+5\right){x}+4a^{3}-6a^{2}-16a+20$ |
| 64.1-a1 |
64.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{8} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$0$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1471.388299$ |
1.028163831 |
\( -548896 a^{2} + 1987376 \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - 4\) , \( a^{3} - 2 a + 1\) , \( 4 a^{3} + 5 a^{2} - 9 a - 9\) , \( 2 a^{2} + 7 a + 5\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(4a^{3}+5a^{2}-9a-9\right){x}+2a^{2}+7a+5$ |
| 64.1-a2 |
64.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{16} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$22.99044218$ |
1.028163831 |
\( 2711191688 a^{2} - 3746774764 \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 3\) , \( -15 a^{3} + 12 a^{2} + 50 a - 50\) , \( -1451 a^{3} + 1696 a^{2} + 5243 a - 6150\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-15a^{3}+12a^{2}+50a-50\right){x}-1451a^{3}+1696a^{2}+5243a-6150$ |
| 64.1-a3 |
64.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{16} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$22.99044218$ |
1.028163831 |
\( -2711191688 a^{2} + 9809183676 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 5 a^{3} - 12 a^{2} - 2 a + 10\) , \( 890 a^{3} - 1696 a^{2} - 1220 a + 2330\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(5a^{3}-12a^{2}-2a+10\right){x}+890a^{3}-1696a^{2}-1220a+2330$ |
| 64.1-a4 |
64.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{8} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$0$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1471.388299$ |
1.028163831 |
\( 548896 a^{2} - 757104 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 3\) , \( 4 a^{3} - 10 a^{2} - 18 a + 31\) , \( 11 a^{3} - 11 a^{2} - 38 a + 43\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(4a^{3}-10a^{2}-18a+31\right){x}+11a^{3}-11a^{2}-38a+43$ |
| 64.1-a5 |
64.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{16} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1471.388299$ |
1.028163831 |
\( 2048 \) |
\( \bigl[0\) , \( a^{2} - 3\) , \( 0\) , \( -a^{2} + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{2}+2\right){x}$ |
| 64.1-a6 |
64.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{8} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$367.8470749$ |
1.028163831 |
\( 78608 \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 0\) , \( 12 a^{3} + 13 a^{2} - 39 a - 44\) , \( 20 a^{3} + 22 a^{2} - 69 a - 79\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(12a^{3}+13a^{2}-39a-44\right){x}+20a^{3}+22a^{2}-69a-79$ |
| 64.1-b1 |
64.1-b |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{16} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.073302756$ |
$949.4144128$ |
1.556184659 |
\( 2711191688 a^{2} - 3746774764 \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 2 a - 4\) , \( a^{2} + a - 3\) , \( -15 a^{3} + 12 a^{2} + 50 a - 50\) , \( 1450 a^{3} - 1696 a^{2} - 5240 a + 6148\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-4\right){x}^{2}+\left(-15a^{3}+12a^{2}+50a-50\right){x}+1450a^{3}-1696a^{2}-5240a+6148$ |
| 64.1-b2 |
64.1-b |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{8} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.146605513$ |
$237.3536032$ |
1.556184659 |
\( -548896 a^{2} + 1987376 \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{3} - 2 a + 1\) , \( 4 a^{3} + 5 a^{2} - 9 a - 9\) , \( -a^{3} - 4 a^{2} - 5 a - 3\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(4a^{3}+5a^{2}-9a-9\right){x}-a^{3}-4a^{2}-5a-3$ |
| 64.1-b3 |
64.1-b |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{8} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.146605513$ |
$237.3536032$ |
1.556184659 |
\( 548896 a^{2} - 757104 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - 3\) , \( a^{3} - 2 a + 1\) , \( 3 a^{3} - 8 a^{2} - 14 a + 23\) , \( -8 a^{3} + 2 a^{2} + 24 a - 18\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(3a^{3}-8a^{2}-14a+23\right){x}-8a^{3}+2a^{2}+24a-18$ |
| 64.1-b4 |
64.1-b |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{16} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.073302756$ |
$949.4144128$ |
1.556184659 |
\( -2711191688 a^{2} + 9809183676 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( 0\) , \( 3 a^{3} - 14 a^{2} + 6 a + 19\) , \( -886 a^{3} + 1683 a^{2} + 1222 a - 2316\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+4\right){x}^{2}+\left(3a^{3}-14a^{2}+6a+19\right){x}-886a^{3}+1683a^{2}+1222a-2316$ |
| 64.1-b5 |
64.1-b |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{16} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.073302756$ |
$949.4144128$ |
1.556184659 |
\( 2048 \) |
\( \bigl[0\) , \( -a^{2} + 3\) , \( 0\) , \( -a^{2} + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{2}+2\right){x}$ |
| 64.1-b6 |
64.1-b |
$6$ |
$8$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{8} \) |
$6.72088$ |
$(a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.146605513$ |
$3797.657651$ |
1.556184659 |
\( 78608 \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - 4 a - 1\) , \( 0\) , \( 11 a^{3} + 10 a^{2} - 38 a - 38\) , \( -45 a^{3} - 52 a^{2} + 162 a + 190\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(11a^{3}+10a^{2}-38a-38\right){x}-45a^{3}-52a^{2}+162a+190$ |
| 79.1-a1 |
79.1-a |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( 79^{4} \) |
$6.90012$ |
$(a^3-2a^2-2a+6)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$111.2348527$ |
1.243643460 |
\( -\frac{5510821934592}{38950081} a^{3} + \frac{6690282255360}{38950081} a^{2} + \frac{19512202644480}{38950081} a - \frac{23230349035840}{38950081} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{3} - 2 a\) , \( -a^{3} - 3 a^{2} + 3 a + 7\) , \( 7 a^{3} + 7 a^{2} - 26 a - 29\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(-a^{3}-3a^{2}+3a+7\right){x}+7a^{3}+7a^{2}-26a-29$ |
| 79.1-a2 |
79.1-a |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( 79^{2} \) |
$6.90012$ |
$(a^3-2a^2-2a+6)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$111.2348527$ |
1.243643460 |
\( \frac{613406825313792}{6241} a^{3} - \frac{721103039411200}{6241} a^{2} - \frac{2219326741908480}{6241} a + \frac{2608975307898560}{6241} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 6 a^{2} + 3 a - 15\) , \( -6 a^{3} - 2 a^{2} + 14 a - 7\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(6a^{2}+3a-15\right){x}-6a^{3}-2a^{2}+14a-7$ |
| 79.1-b1 |
79.1-b |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( 79^{2} \) |
$6.90012$ |
$(a^3-2a^2-2a+6)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$155.2093026$ |
1.735292756 |
\( -\frac{51970850297981607}{6241} a^{3} + \frac{98854431667475790}{6241} a^{2} + \frac{71821948689392780}{6241} a - \frac{136613464610314700}{6241} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{2} - 3\) , \( 0\) , \( -4 a - 8\) , \( -7 a^{3} - 10 a^{2} + 18 a + 22\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-4a-8\right){x}-7a^{3}-10a^{2}+18a+22$ |
| 79.1-b2 |
79.1-b |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$6.90012$ |
$(a^3-2a^2-2a+6)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$310.4186052$ |
1.735292756 |
\( -\frac{78157332}{79} a^{3} + \frac{148661440}{79} a^{2} + \frac{107998540}{79} a - \frac{205350795}{79} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{2} - 3\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(a+2\right){x}$ |
| 79.1-c1 |
79.1-c |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( 79^{2} \) |
$6.90012$ |
$(a^3-2a^2-2a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.034185335$ |
$921.5828295$ |
1.408929375 |
\( -\frac{51970850297981607}{6241} a^{3} + \frac{98854431667475790}{6241} a^{2} + \frac{71821948689392780}{6241} a - \frac{136613464610314700}{6241} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 2 a - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - 6 a - 10\) , \( 3 a^{3} + 3 a^{2} - 11 a - 9\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-3\right){x}^{2}+\left(a^{2}-6a-10\right){x}+3a^{3}+3a^{2}-11a-9$ |
| 79.1-c2 |
79.1-c |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$6.90012$ |
$(a^3-2a^2-2a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.068370671$ |
$921.5828295$ |
1.408929375 |
\( -\frac{78157332}{79} a^{3} + \frac{148661440}{79} a^{2} + \frac{107998540}{79} a - \frac{205350795}{79} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 2 a - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - a\) , \( a^{3} + 3 a^{2} - 3 a - 7\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-3\right){x}^{2}+\left(a^{2}-a\right){x}+a^{3}+3a^{2}-3a-7$ |
| 79.1-d1 |
79.1-d |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( 79^{4} \) |
$6.90012$ |
$(a^3-2a^2-2a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.034572360$ |
$582.6052374$ |
1.801558660 |
\( -\frac{5510821934592}{38950081} a^{3} + \frac{6690282255360}{38950081} a^{2} + \frac{19512202644480}{38950081} a - \frac{23230349035840}{38950081} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + 3\) , \( a^{2} + a - 2\) , \( -a^{3} - 4 a^{2} + 3 a + 9\) , \( -8 a^{3} - 11 a^{2} + 29 a + 37\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{3}-4a^{2}+3a+9\right){x}-8a^{3}-11a^{2}+29a+37$ |
| 79.1-d2 |
79.1-d |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( 79^{2} \) |
$6.90012$ |
$(a^3-2a^2-2a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.069144720$ |
$582.6052374$ |
1.801558660 |
\( \frac{613406825313792}{6241} a^{3} - \frac{721103039411200}{6241} a^{2} - \frac{2219326741908480}{6241} a + \frac{2608975307898560}{6241} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - a - 4\) , \( a^{2} + a - 2\) , \( -a^{3} + 4 a^{2} + 6 a - 9\) , \( 6 a^{3} + 2 a^{2} - 15 a + 5\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{3}+4a^{2}+6a-9\right){x}+6a^{3}+2a^{2}-15a+5$ |
| 79.2-a1 |
79.2-a |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$6.90012$ |
$(a^3+2a^2-4a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$111.2348527$ |
1.243643460 |
\( -\frac{379106265967104}{6241} a^{3} + \frac{721103039411200}{6241} a^{2} + \frac{523911972587520}{6241} a - \frac{996539889157440}{6241} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - 3\) , \( a^{2} + a - 2\) , \( 3 a^{3} - 6 a^{2} - 9 a + 15\) , \( -4 a^{3} + 2 a^{2} + 18 a - 17\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(3a^{3}-6a^{2}-9a+15\right){x}-4a^{3}+2a^{2}+18a-17$ |
| 79.2-a2 |
79.2-a |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( 79^{4} \) |
$6.90012$ |
$(a^3+2a^2-4a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$111.2348527$ |
1.243643460 |
\( \frac{2979736840704}{38950081} a^{3} - \frac{6690282255360}{38950081} a^{2} - \frac{3428388587520}{38950081} a + \frac{10221062240960}{38950081} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + 3\) , \( a^{3} - 2 a\) , \( a^{2} - 3\) , \( -5 a^{3} - 9 a^{2} + 8 a + 11\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(a^{2}-3\right){x}-5a^{3}-9a^{2}+8a+11$ |
| 79.2-b1 |
79.2-b |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$6.90012$ |
$(a^3+2a^2-4a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$155.2093026$ |
1.735292756 |
\( -\frac{84090602204552041}{6241} a^{3} - \frac{98854431667475790}{6241} a^{2} + \frac{304242656911637730}{6241} a + \frac{357658693727064250}{6241} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 2\) , \( 0\) , \( -4 a^{3} + 12 a - 8\) , \( -3 a^{3} + 10 a^{2} + 16 a - 28\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-4a^{3}+12a-8\right){x}-3a^{3}+10a^{2}+16a-28$ |
| 79.2-b2 |
79.2-b |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$6.90012$ |
$(a^3+2a^2-4a-4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$310.4186052$ |
1.735292756 |
\( -\frac{126473456}{79} a^{3} - \frac{148661440}{79} a^{2} + \frac{457577700}{79} a + \frac{537956405}{79} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 2\) , \( 0\) , \( a^{3} - 3 a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(a^{3}-3a+2\right){x}$ |
| 79.2-c1 |
79.2-c |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$6.90012$ |
$(a^3+2a^2-4a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.034185335$ |
$921.5828295$ |
1.408929375 |
\( -\frac{84090602204552041}{6241} a^{3} - \frac{98854431667475790}{6241} a^{2} + \frac{304242656911637730}{6241} a + \frac{357658693727064250}{6241} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( -4 a^{3} + 12 a - 9\) , \( -a^{3} - 10 a^{2} - 4 a + 19\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-3\right){x}{y}+\left(a^{3}+a^{2}-2a-3\right){y}={x}^{3}+{x}^{2}+\left(-4a^{3}+12a-9\right){x}-a^{3}-10a^{2}-4a+19$ |
| 79.2-c2 |
79.2-c |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$6.90012$ |
$(a^3+2a^2-4a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.068370671$ |
$921.5828295$ |
1.408929375 |
\( -\frac{126473456}{79} a^{3} - \frac{148661440}{79} a^{2} + \frac{457577700}{79} a + \frac{537956405}{79} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a^{3} - 3 a + 1\) , \( a^{3} - 3 a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-3\right){x}{y}+\left(a^{3}+a^{2}-2a-3\right){y}={x}^{3}+{x}^{2}+\left(a^{3}-3a+1\right){x}+a^{3}-3a+1$ |
| 79.2-d1 |
79.2-d |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( 79^{2} \) |
$6.90012$ |
$(a^3+2a^2-4a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.069144720$ |
$582.6052374$ |
1.801558660 |
\( -\frac{379106265967104}{6241} a^{3} + \frac{721103039411200}{6241} a^{2} + \frac{523911972587520}{6241} a - \frac{996539889157440}{6241} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( a^{3} - 2 a\) , \( 3 a^{3} - 9 a^{2} - 9 a + 25\) , \( 7 a^{3} - 10 a^{2} - 27 a + 37\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+4\right){x}^{2}+\left(3a^{3}-9a^{2}-9a+25\right){x}+7a^{3}-10a^{2}-27a+37$ |
| 79.2-d2 |
79.2-d |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( 79^{4} \) |
$6.90012$ |
$(a^3+2a^2-4a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.034572360$ |
$582.6052374$ |
1.801558660 |
\( \frac{2979736840704}{38950081} a^{3} - \frac{6690282255360}{38950081} a^{2} - \frac{3428388587520}{38950081} a + \frac{10221062240960}{38950081} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + 4 a^{2} - 4 a - 11\) , \( 6 a^{3} + 11 a^{2} - 11 a - 18\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(a^{3}+4a^{2}-4a-11\right){x}+6a^{3}+11a^{2}-11a-18$ |
| 79.3-a1 |
79.3-a |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.3 |
\( 79 \) |
\( 79^{2} \) |
$6.90012$ |
$(a^3-2a^2-4a+4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$111.2348527$ |
1.243643460 |
\( \frac{379106265967104}{6241} a^{3} + \frac{721103039411200}{6241} a^{2} - \frac{523911972587520}{6241} a - \frac{996539889157440}{6241} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 2\) , \( -5 a^{3} - 6 a^{2} + 14 a + 15\) , \( 3 a^{3} + 2 a^{2} - 16 a - 17\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-5a^{3}-6a^{2}+14a+15\right){x}+3a^{3}+2a^{2}-16a-17$ |
| 79.3-a2 |
79.3-a |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.3 |
\( 79 \) |
\( 79^{4} \) |
$6.90012$ |
$(a^3-2a^2-4a+4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$111.2348527$ |
1.243643460 |
\( -\frac{2979736840704}{38950081} a^{3} - \frac{6690282255360}{38950081} a^{2} + \frac{3428388587520}{38950081} a + \frac{10221062240960}{38950081} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} - a + 3\) , \( a^{3} - 2 a\) , \( -a^{3} + a^{2} + a - 3\) , \( 5 a^{3} - 9 a^{2} - 8 a + 11\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-a^{3}+a^{2}+a-3\right){x}+5a^{3}-9a^{2}-8a+11$ |
| 79.3-b1 |
79.3-b |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.3 |
\( 79 \) |
\( 79^{2} \) |
$6.90012$ |
$(a^3-2a^2-4a+4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$155.2093026$ |
1.735292756 |
\( \frac{84090602204552041}{6241} a^{3} - \frac{98854431667475790}{6241} a^{2} - \frac{304242656911637730}{6241} a + \frac{357658693727064250}{6241} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( 0\) , \( 4 a^{3} - 12 a - 8\) , \( 3 a^{3} + 10 a^{2} - 16 a - 28\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(4a^{3}-12a-8\right){x}+3a^{3}+10a^{2}-16a-28$ |
| 79.3-b2 |
79.3-b |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
79.3 |
\( 79 \) |
\( -79 \) |
$6.90012$ |
$(a^3-2a^2-4a+4)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$310.4186052$ |
1.735292756 |
\( \frac{126473456}{79} a^{3} - \frac{148661440}{79} a^{2} - \frac{457577700}{79} a + \frac{537956405}{79} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( 0\) , \( -a^{3} + 3 a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-a^{3}+3a+2\right){x}$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
