| 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 |
| 9.1-CMa1 |
9.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.43777$ |
$(-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.326567372$ |
0.287814748 |
\( 8000 \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}$ |
| 9.3-CMa1 |
9.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.43777$ |
$(a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.326567372$ |
0.287814748 |
\( 8000 \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-1\right){x}$ |
| 121.1-CMa1 |
121.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$0.83826$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$11$ |
11Cs.3.1 |
$1$ |
\( 2 \) |
$1$ |
$3.826175023$ |
1.352757152 |
\( 8000 \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 2 a + 3\) , \( a - 3\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(2a+3\right){x}+a-3$ |
| 121.3-CMa1 |
121.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
121.3 |
\( 11^{2} \) |
\( 11^{6} \) |
$0.83826$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$11$ |
11Cs.3.1 |
$1$ |
\( 2 \) |
$1$ |
$3.826175023$ |
1.352757152 |
\( 8000 \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -3 a + 3\) , \( -a - 3\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3a+3\right){x}-a-3$ |
| 144.1-CMa1 |
144.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$0.87554$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$3.663283686$ |
1.295166367 |
\( 8000 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 2\) , \( -2 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-2\right){x}-2a-4$ |
| 144.3-CMa1 |
144.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
144.3 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$0.87554$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$3.663283686$ |
1.295166367 |
\( 8000 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 2\) , \( 2 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-2\right){x}+2a-4$ |
| 256.1-CMb1 |
256.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$1.01098$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$6.344993467$ |
1.121646976 |
\( 8000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}+a$ |
| 256.1-CMa1 |
256.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$1.01098$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$6.344993467$ |
1.121646976 |
\( 8000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( -a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}-a$ |
| 361.1-CMa1 |
361.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
361.1 |
\( 19^{2} \) |
\( 19^{6} \) |
$1.10169$ |
$(-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$19$ |
19Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$2.911282665$ |
1.029293857 |
\( 8000 \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -2 a - 7\) , \( -4\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-7\right){x}-4$ |
| 361.3-CMa1 |
361.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
361.3 |
\( 19^{2} \) |
\( 19^{6} \) |
$1.10169$ |
$(3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$19$ |
19Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$2.911282665$ |
1.029293857 |
\( 8000 \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( a - 7\) , \( -4\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a-7\right){x}-4$ |
| 1024.1-CMb1 |
1024.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.486587907$ |
3.172496733 |
\( 8000 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( -1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3{x}-1$ |
| 1024.1-CMa1 |
1024.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.115260390$ |
$4.486587907$ |
1.462652852 |
\( 8000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}+1$ |
| 1849.1-CMa1 |
1849.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1849.1 |
\( 43^{2} \) |
\( 43^{6} \) |
$1.65736$ |
$(-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$43$ |
43Cs.9.1 |
$1$ |
\( 2 \) |
$1$ |
$1.935204865$ |
0.684198241 |
\( 8000 \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 13 a + 3\) , \( 2 a + 29\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(13a+3\right){x}+2a+29$ |
| 1849.3-CMa1 |
1849.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1849.3 |
\( 43^{2} \) |
\( 43^{6} \) |
$1.65736$ |
$(3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$43$ |
43Cs.9.1 |
$1$ |
\( 2 \) |
$1$ |
$1.935204865$ |
0.684198241 |
\( 8000 \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -14 a + 3\) , \( -2 a + 29\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-14a+3\right){x}-2a+29$ |
| 1936.1-CMa1 |
1936.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1936.1 |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{6} \) |
$1.67652$ |
$(a), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$1.913087511$ |
0.676378576 |
\( 8000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 10 a + 12\) , \( 8 a - 22\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(10a+12\right){x}+8a-22$ |
| 1936.3-CMa1 |
1936.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1936.3 |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{6} \) |
$1.67652$ |
$(a), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$1.913087511$ |
0.676378576 |
\( 8000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -10 a + 12\) , \( -8 a - 22\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-10a+12\right){x}-8a-22$ |
| 2601.1-CMa1 |
2601.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{6} \) |
$1.80496$ |
$(-a-1), (-2a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.222088609$ |
$1.776953597$ |
2.232427484 |
\( 8000 \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 5 a + 19\) , \( 14 a - 12\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a+19\right){x}+14a-12$ |
| 2601.3-CMa1 |
2601.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.3 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{6} \) |
$1.80496$ |
$(-a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.776953597$ |
2.512991876 |
\( 8000 \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -5 a - 20\) , \( 3 a + 37\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-5a-20\right){x}+3a+37$ |
| 2601.7-CMa1 |
2601.7-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.7 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{6} \) |
$1.80496$ |
$(a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.776953597$ |
2.512991876 |
\( 8000 \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 4 a - 20\) , \( -4 a + 37\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(4a-20\right){x}-4a+37$ |
| 2601.9-CMa1 |
2601.9-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.9 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{6} \) |
$1.80496$ |
$(a-1), (2a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.222088609$ |
$1.776953597$ |
2.232427484 |
\( 8000 \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -6 a + 19\) , \( -14 a - 12\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a+19\right){x}-14a-12$ |
| 3481.1-CMa1 |
3481.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3481.1 |
\( 59^{2} \) |
\( 59^{6} \) |
$1.94138$ |
$(-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$59$ |
59Cs.3.1 |
$1$ |
\( 2 \) |
$1$ |
$1.652095579$ |
0.584103993 |
\( 8000 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -13 a - 16\) , \( 29 a + 18\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-13a-16\right){x}+29a+18$ |
| 3481.3-CMa1 |
3481.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3481.3 |
\( 59^{2} \) |
\( 59^{6} \) |
$1.94138$ |
$(-5a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$59$ |
59Cs.3.1 |
$1$ |
\( 2 \) |
$1$ |
$1.652095579$ |
0.584103993 |
\( 8000 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 12 a - 16\) , \( -30 a + 18\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(12a-16\right){x}-30a+18$ |
| 4489.1-CMa1 |
4489.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4489.1 |
\( 67^{2} \) |
\( 67^{6} \) |
$2.06881$ |
$(-3a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$67$ |
67Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.550328652$ |
0.548123951 |
\( 8000 \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -17 a + 13\) , \( 2 a + 32\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-17a+13\right){x}+2a+32$ |
| 4489.3-CMa1 |
4489.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4489.3 |
\( 67^{2} \) |
\( 67^{6} \) |
$2.06881$ |
$(3a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$67$ |
67Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.550328652$ |
0.548123951 |
\( 8000 \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 16 a + 13\) , \( -2 a + 32\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(16a+13\right){x}-2a+32$ |
| 5625.1-CMa1 |
5625.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5625.1 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{12} \) |
$2.18884$ |
$(-a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.465313474$ |
2.072266188 |
\( 8000 \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 20 a - 10\) , \( -48 a - 28\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(20a-10\right){x}-48a-28$ |
| 5625.3-CMa1 |
5625.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{12} \) |
$2.18884$ |
$(a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.465313474$ |
2.072266188 |
\( 8000 \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -21 a - 10\) , \( 47 a - 28\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-21a-10\right){x}+47a-28$ |
| 5776.1-CMa1 |
5776.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.1 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{6} \) |
$2.20338$ |
$(a), (-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$1.455641332$ |
0.514646928 |
\( 8000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 29\) , \( -37 a - 40\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-10a-29\right){x}-37a-40$ |
| 5776.3-CMa1 |
5776.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.3 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{6} \) |
$2.20338$ |
$(a), (3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$1.455641332$ |
0.514646928 |
\( 8000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 29\) , \( 37 a - 40\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(10a-29\right){x}+37a-40$ |
| 6889.1-CMa1 |
6889.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6889.1 |
\( 83^{2} \) |
\( 83^{6} \) |
$2.30262$ |
$(a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$83$ |
83Cs.3.1 |
$9$ |
\( 2 \) |
$1$ |
$1.392907025$ |
4.432203013 |
\( 8000 \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 7 a + 33\) , \( 45 a - 26\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(7a+33\right){x}+45a-26$ |
| 6889.3-CMa1 |
6889.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6889.3 |
\( 83^{2} \) |
\( 83^{6} \) |
$2.30262$ |
$(a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$83$ |
83Cs.3.1 |
$9$ |
\( 2 \) |
$1$ |
$1.392907025$ |
4.432203013 |
\( 8000 \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -8 a + 33\) , \( -45 a - 26\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-8a+33\right){x}-45a-26$ |
| 9216.1-CMb1 |
9216.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.47639$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.590332735$ |
1.831641843 |
\( 8000 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a + 3\) , \( a - 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a+3\right){x}+a-5$ |
| 9216.1-CMa1 |
9216.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.47639$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.590332735$ |
1.831641843 |
\( 8000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a + 3\) , \( -a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a+3\right){x}-a+5$ |
| 9216.3-CMb1 |
9216.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.3 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.47639$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.590332735$ |
1.831641843 |
\( 8000 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a + 3\) , \( -a - 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a+3\right){x}-a-5$ |
| 9216.3-CMa1 |
9216.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.3 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.47639$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.590332735$ |
1.831641843 |
\( 8000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 6 a + 3\) , \( a + 5\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(6a+3\right){x}+a+5$ |
| 9801.7-CMa1 |
9801.7-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9801.7 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{6} \) |
$2.51479$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.275391674$ |
1.803676203 |
\( 8000 \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 22 a + 27\) , \( -27 a + 74\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(22a+27\right){x}-27a+74$ |
| 9801.9-CMa1 |
9801.9-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9801.9 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{6} \) |
$2.51479$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.275391674$ |
1.803676203 |
\( 8000 \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -23 a + 27\) , \( 27 a + 74\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-23a+27\right){x}+27a+74$ |
| 11449.1-CMa1 |
11449.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11449.1 |
\( 107^{2} \) |
\( 107^{6} \) |
$2.61442$ |
$(7a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$107$ |
107Cs.3.1 |
$1$ |
\( 2 \) |
$1$ |
$1.226787341$ |
0.433734824 |
\( 8000 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 17 a - 36\) , \( 52 a - 58\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(17a-36\right){x}+52a-58$ |
| 11449.3-CMa1 |
11449.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11449.3 |
\( 107^{2} \) |
\( 107^{6} \) |
$2.61442$ |
$(7a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$107$ |
107Cs.3.1 |
$1$ |
\( 2 \) |
$1$ |
$1.226787341$ |
0.433734824 |
\( 8000 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -18 a - 36\) , \( -53 a - 58\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-18a-36\right){x}-53a-58$ |
| 15129.1-CMa1 |
15129.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15129.1 |
\( 3^{2} \cdot 41^{2} \) |
\( 3^{6} \cdot 41^{6} \) |
$2.80308$ |
$(-a-1), (-4a-3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.995069022$ |
$1.144217588$ |
6.440755524 |
\( 8000 \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -30 a - 30\) , \( -93 a + 4\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-30a-30\right){x}-93a+4$ |
| 15129.3-CMa1 |
15129.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15129.3 |
\( 3^{2} \cdot 41^{2} \) |
\( 3^{6} \cdot 41^{6} \) |
$2.80308$ |
$(-a-1), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.144217588$ |
1.618168031 |
\( 8000 \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -10 a + 49\) , \( -100 a - 45\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a+49\right){x}-100a-45$ |
| 15129.7-CMa1 |
15129.7-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15129.7 |
\( 3^{2} \cdot 41^{2} \) |
\( 3^{6} \cdot 41^{6} \) |
$2.80308$ |
$(a-1), (-4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.144217588$ |
1.618168031 |
\( 8000 \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 9 a + 49\) , \( 100 a - 45\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a+49\right){x}+100a-45$ |
| 15129.9-CMa1 |
15129.9-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15129.9 |
\( 3^{2} \cdot 41^{2} \) |
\( 3^{6} \cdot 41^{6} \) |
$2.80308$ |
$(a-1), (4a-3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.995069022$ |
$1.144217588$ |
6.440755524 |
\( 8000 \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 29 a - 30\) , \( 92 a + 4\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(29a-30\right){x}+92a+4$ |
| 17161.1-CMa1 |
17161.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
17161.1 |
\( 131^{2} \) |
\( 131^{6} \) |
$2.89281$ |
$(-5a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$131$ |
131Cs.3.1 |
$1$ |
\( 2 \) |
$1$ |
$1.108729306$ |
0.391995005 |
\( 8000 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 37 a + 14\) , \( -47 a - 127\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(37a+14\right){x}-47a-127$ |
| 17161.3-CMa1 |
17161.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
17161.3 |
\( 131^{2} \) |
\( 131^{6} \) |
$2.89281$ |
$(5a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$131$ |
131Cs.3.1 |
$1$ |
\( 2 \) |
$1$ |
$1.108729306$ |
0.391995005 |
\( 8000 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -38 a + 14\) , \( 46 a - 127\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-38a+14\right){x}+46a-127$ |
| 19321.1-CMa1 |
19321.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19321.1 |
\( 139^{2} \) |
\( 139^{6} \) |
$2.97983$ |
$(-3a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$139$ |
139Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.076350643$ |
0.380547419 |
\( 8000 \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 28 a + 43\) , \( -76 a + 131\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(28a+43\right){x}-76a+131$ |
| 19321.3-CMa1 |
19321.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19321.3 |
\( 139^{2} \) |
\( 139^{6} \) |
$2.97983$ |
$(3a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$139$ |
139Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.076350643$ |
0.380547419 |
\( 8000 \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -29 a + 43\) , \( 76 a + 131\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-29a+43\right){x}+76a+131$ |
| 20736.3-CMb1 |
20736.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.114997822$ |
1.495529302 |
\( 8000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( 14 a\bigr] \) |
${y}^2={x}^{3}+15{x}+14a$ |
| 20736.3-CMa1 |
20736.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.114997822$ |
1.495529302 |
\( 8000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( -14 a\bigr] \) |
${y}^2={x}^{3}+15{x}-14a$ |
| 21609.1-CMa1 |
21609.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{6} \cdot 7^{12} \) |
$3.06438$ |
$(-a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.046652481$ |
1.480190134 |
\( 8000 \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 40 a - 20\) , \( 97 a + 21\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(40a-20\right){x}+97a+21$ |
| 21609.3-CMa1 |
21609.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
21609.3 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{6} \cdot 7^{12} \) |
$3.06438$ |
$(a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.046652481$ |
1.480190134 |
\( 8000 \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -41 a - 20\) , \( -98 a + 21\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-41a-20\right){x}-98a+21$ |
*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.
