| 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 |
| 64.1-a1 |
64.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$966.6894380$ |
1.258710205 |
\( 52395098160 a^{3} + 101219598208 a^{2} - 14039121856 a - 27121655032 \) |
\( \bigl[a^{2} - 1\) , \( a^{2} + a - 2\) , \( a^{3} - 3 a\) , \( 7 a^{3} - a^{2} - 21 a + 2\) , \( -9 a^{3} + 7 a^{2} + 24 a - 2\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(7a^{3}-a^{2}-21a+2\right){x}-9a^{3}+7a^{2}+24a-2$ |
| 64.1-a2 |
64.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$966.6894380$ |
1.258710205 |
\( -52395098160 a^{3} + 101219598208 a^{2} + 14039121856 a - 27121655032 \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{3} - 3 a\) , \( -7 a^{3} - a^{2} + 19 a + 2\) , \( 9 a^{3} + 7 a^{2} - 24 a - 2\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-7a^{3}-a^{2}+19a+2\right){x}+9a^{3}+7a^{2}-24a-2$ |
| 64.1-a3 |
64.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1933.378876$ |
1.258710205 |
\( 241408 a^{2} - 62784 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{2} + 2 a - 1\) , \( a^{3} - 3 a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(a^{2}+2a-1\right){x}+a^{3}-3a+1$ |
| 64.1-a4 |
64.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$483.3447190$ |
1.258710205 |
\( -241408 a^{2} + 902848 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -5 a^{3} + a^{2} + 17 a - 7\) , \( -5 a^{3} + 2 a^{2} + 17 a - 11\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-5a^{3}+a^{2}+17a-7\right){x}-5a^{3}+2a^{2}+17a-11$ |
| 64.1-a5 |
64.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$60.41808987$ |
1.258710205 |
\( 195541270784 a^{3} - 101219598208 a^{2} - 729769984976 a + 377756737800 \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 6 a^{3} + 3 a^{2} - 18 a - 7\) , \( 19 a^{3} + 9 a^{2} - 61 a - 32\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(6a^{3}+3a^{2}-18a-7\right){x}+19a^{3}+9a^{2}-61a-32$ |
| 64.1-a6 |
64.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$60.41808987$ |
1.258710205 |
\( -195541270784 a^{3} - 101219598208 a^{2} + 729769984976 a + 377756737800 \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -6 a^{3} + 3 a^{2} + 16 a - 7\) , \( -19 a^{3} + 9 a^{2} + 59 a - 32\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-6a^{3}+3a^{2}+16a-7\right){x}-19a^{3}+9a^{2}+59a-32$ |
| 64.1-b1 |
64.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.444312937$ |
$378.1454402$ |
1.750155326 |
\( 1728 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{2} - a - 2\) , \( 0\) , \( -5 a^{3} - a^{2} + 19 a + 10\) , \( 2 a^{3} + 2 a^{2} - 7 a - 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-5a^{3}-a^{2}+19a+10\right){x}+2a^{3}+2a^{2}-7a-4$ |
| 64.1-b2 |
64.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.222156468$ |
$1512.581761$ |
1.750155326 |
\( 1728 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{2} - a - 2\) , \( 0\) , \( -a^{3} - a^{2} - a\) , \( -2 a^{3} - 3 a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-a^{3}-a^{2}-a\right){x}-2a^{3}-3a^{2}+a+1$ |
| 64.1-b3 |
64.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.444312937$ |
$189.0727201$ |
1.750155326 |
\( 287496 \) |
\( \bigl[a^{3} - 3 a\) , \( 1\) , \( 0\) , \( -2\) , \( -3\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+{x}^{2}-2{x}-3$ |
| 64.1-b4 |
64.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.111078234$ |
$3025.163522$ |
1.750155326 |
\( 287496 \) |
\( \bigl[a^{3} - 3 a\) , \( 1\) , \( a^{3} - 3 a\) , \( -3\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+{x}^{2}-3{x}$ |
| 64.1-b5 |
64.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$7.21360$ |
$(a^3-4a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.222156468$ |
$1512.581761$ |
1.750155326 |
\( 29071392966 a^{3} - 87214178898 a + 41113158120 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 1\) , \( -16 a^{3} + 3 a^{2} + 63 a - 28\) , \( 19 a^{3} + 21 a^{2} - 146 a + 68\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-16a^{3}+3a^{2}+63a-28\right){x}+19a^{3}+21a^{2}-146a+68$ |
| 64.1-b6 |
64.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$7.21360$ |
$(a^3-4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 1 \) |
$0.888625874$ |
$23.63409001$ |
1.750155326 |
\( 29071392966 a^{3} - 87214178898 a + 41113158120 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a^{3} - 4 a + 1\) , \( -15 a^{3} + 5 a^{2} + 58 a - 31\) , \( -35 a^{3} - 17 a^{2} + 209 a - 99\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-1\right){x}^{2}+\left(-15a^{3}+5a^{2}+58a-31\right){x}-35a^{3}-17a^{2}+209a-99$ |
| 64.1-b7 |
64.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$7.21360$ |
$(a^3-4a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.222156468$ |
$1512.581761$ |
1.750155326 |
\( -29071392966 a^{3} + 87214178898 a + 41113158120 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a + 1\) , \( 14 a^{3} + 3 a^{2} - 59 a - 29\) , \( -16 a^{3} + 20 a^{2} + 117 a + 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(14a^{3}+3a^{2}-59a-29\right){x}-16a^{3}+20a^{2}+117a+53$ |
| 64.1-b8 |
64.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$7.21360$ |
$(a^3-4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 1 \) |
$0.888625874$ |
$23.63409001$ |
1.750155326 |
\( -29071392966 a^{3} + 87214178898 a + 41113158120 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 5 a - 1\) , \( 0\) , \( 14 a^{3} + 5 a^{2} - 61 a - 30\) , \( 30 a^{3} - 16 a^{2} - 177 a - 83\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}={x}^{3}+\left(a^{3}+a^{2}-5a-1\right){x}^{2}+\left(14a^{3}+5a^{2}-61a-30\right){x}+30a^{3}-16a^{2}-177a-83$ |
| 64.1-c1 |
64.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$60.41808987$ |
1.258710205 |
\( 52395098160 a^{3} + 101219598208 a^{2} - 14039121856 a - 27121655032 \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - a - 1\) , \( a^{3} - 3 a\) , \( 5 a^{3} - 19 a + 1\) , \( 8 a^{3} - 10 a^{2} - 11 a + 1\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(5a^{3}-19a+1\right){x}+8a^{3}-10a^{2}-11a+1$ |
| 64.1-c2 |
64.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$60.41808987$ |
1.258710205 |
\( -52395098160 a^{3} + 101219598208 a^{2} + 14039121856 a - 27121655032 \) |
\( \bigl[a^{2} - 1\) , \( a^{2} + a - 1\) , \( a^{3} - 3 a\) , \( -5 a^{3} + 17 a + 1\) , \( -8 a^{3} - 10 a^{2} + 11 a + 1\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-5a^{3}+17a+1\right){x}-8a^{3}-10a^{2}+11a+1$ |
| 64.1-c3 |
64.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$483.3447190$ |
1.258710205 |
\( 241408 a^{2} - 62784 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 0\) , \( -3 a^{3} - a^{2} + 9 a\) , \( -2 a^{3} - 6 a^{2} - 3 a + 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-3a^{3}-a^{2}+9a\right){x}-2a^{3}-6a^{2}-3a+2$ |
| 64.1-c4 |
64.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1933.378876$ |
1.258710205 |
\( -241408 a^{2} + 902848 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( 0\) , \( -2 a^{3} + 5 a^{2} + 14 a - 6\) , \( 11 a^{3} - 3 a^{2} - 37 a + 19\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(-2a^{3}+5a^{2}+14a-6\right){x}+11a^{3}-3a^{2}-37a+19$ |
| 64.1-c5 |
64.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$966.6894380$ |
1.258710205 |
\( 195541270784 a^{3} - 101219598208 a^{2} - 729769984976 a + 377756737800 \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 4 a^{3} + 2 a^{2} - 12 a - 6\) , \( -18 a^{3} - 9 a^{2} + 68 a + 35\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(4a^{3}+2a^{2}-12a-6\right){x}-18a^{3}-9a^{2}+68a+35$ |
| 64.1-c6 |
64.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$7.21360$ |
$(a^3-4a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$966.6894380$ |
1.258710205 |
\( -195541270784 a^{3} - 101219598208 a^{2} + 729769984976 a + 377756737800 \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -4 a^{3} + 2 a^{2} + 10 a - 6\) , \( 18 a^{3} - 9 a^{2} - 70 a + 35\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-4a^{3}+2a^{2}+10a-6\right){x}+18a^{3}-9a^{2}-70a+35$ |
*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.
