| 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 |
| 16.1-CMa1 |
16.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.47284$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$6.540964764$ |
0.309031537 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+{x}$ |
| 16.5-CMa1 |
16.5-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16.5 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.47284$ |
$(-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$6.540964764$ |
0.309031537 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$ |
| 49.1-CMa1 |
49.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$0.62551$ |
$(-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$7$ |
7B.1.4[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$4.944504600$ |
0.934423537 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1$ |
| 64.1-CMa1 |
64.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{18} \) |
$0.66870$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.625160540$ |
0.874073183 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 2 a + 2\) , \( -2 a + 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+2\right){x}-2a+3$ |
| 64.7-CMa1 |
64.7-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
64.7 |
\( 2^{6} \) |
\( 2^{18} \) |
$0.66870$ |
$(-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.625160540$ |
0.874073183 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -a + 2\) , \( 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-a+2\right){x}+3$ |
| 121.1-CMa1 |
121.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$0.78412$ |
$(-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$11$ |
11Cs.3.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.944350161$ |
0.745412115 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -3 a\) , \( 2 a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-3a{x}+2a-2$ |
| 121.3-CMa1 |
121.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
121.3 |
\( 11^{2} \) |
\( 11^{6} \) |
$0.78412$ |
$(2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$11$ |
11Cs.3.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.944350161$ |
0.745412115 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 2 a - 2\) , \( -3 a + 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(2a-2\right){x}-3a+1$ |
| 529.1-CMa1 |
529.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
529.1 |
\( 23^{2} \) |
\( 23^{6} \) |
$1.13384$ |
$(-2a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$23$ |
23Cs.2.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.727770870$ |
0.515500239 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5 a + 5\) , \( 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-5a+5\right){x}+8$ |
| 529.3-CMa1 |
529.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
529.3 |
\( 23^{2} \) |
\( 23^{6} \) |
$1.13384$ |
$(2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$23$ |
23Cs.2.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.727770870$ |
0.515500239 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 5 a\) , \( 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+5a{x}+8$ |
| 1024.5-CMa1 |
1024.5-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.5 |
\( 2^{10} \) |
\( 2^{30} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$2.312580270$ |
1.748146366 |
\( -3375 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 5 a - 10\) , \( 10 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(5a-10\right){x}+10a-12$ |
| 1024.7-CMa1 |
1024.7-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.7 |
\( 2^{10} \) |
\( 2^{30} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$2.312580270$ |
1.748146366 |
\( -3375 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5 a - 5\) , \( -10 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-5a-5\right){x}-10a-2$ |
| 1296.1-CMa1 |
1296.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.41853$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$2.180321588$ |
1.648168200 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -8 a + 7\) , \( 12 a - 25\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a+7\right){x}+12a-25$ |
| 1296.5-CMa1 |
1296.5-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1296.5 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.41853$ |
$(-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$2.180321588$ |
1.648168200 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 9 a - 3\) , \( -4 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(9a-3\right){x}-4a-16$ |
| 1849.1-CMa1 |
1849.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1849.1 |
\( 43^{2} \) |
\( 43^{6} \) |
$1.55032$ |
$(-2a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$43$ |
43Cs.9.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.994975550$ |
0.377014941 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -8 a + 13\) , \( -4 a - 22\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-8a+13\right){x}-4a-22$ |
| 1849.3-CMa1 |
1849.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1849.3 |
\( 43^{2} \) |
\( 43^{6} \) |
$1.55032$ |
$(2a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$43$ |
43Cs.9.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.994975550$ |
0.377014941 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 7 a + 5\) , \( 3 a - 26\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(7a+5\right){x}+3a-26$ |
| 3136.1-CMa1 |
3136.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{6} \) |
$1.76922$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.748146366$ |
1.321474440 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -10 a - 4\) , \( -17 a + 6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a-4\right){x}-17a+6$ |
| 3136.7-CMa1 |
3136.7-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3136.7 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{6} \) |
$1.76922$ |
$(-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.748146366$ |
1.321474440 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 10 a - 15\) , \( 27 a - 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(10a-15\right){x}+27a-26$ |
| 3969.1-CMa1 |
3969.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{6} \) |
$1.87654$ |
$(-2a+1), (3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.336279925$ |
$1.648168200$ |
1.675882015 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -20\) , \( 46\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-20{x}+46$ |
| 4096.7-CMb1 |
4096.7-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{36} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.635241191$ |
1.236126150 |
\( -3375 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 20\) , \( -32 a + 16\bigr] \) |
${y}^2={x}^{3}+20{x}-32a+16$ |
| 4096.7-CMa1 |
4096.7-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{36} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.635241191$ |
1.236126150 |
\( -3375 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 20\) , \( 32 a - 16\bigr] \) |
${y}^2={x}^{3}+20{x}+32a-16$ |
| 4489.1-CMa1 |
4489.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4489.1 |
\( 67^{2} \) |
\( 67^{6} \) |
$1.93520$ |
$(-6a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$67$ |
67Cs.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.598212061$ |
0.302033689 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 7 a - 22\) , \( 21 a - 39\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(7a-22\right){x}+21a-39$ |
| 4489.3-CMa1 |
4489.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4489.3 |
\( 67^{2} \) |
\( 67^{6} \) |
$1.93520$ |
$(6a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$67$ |
67Cs.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.598212061$ |
0.302033689 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -8 a - 15\) , \( -22 a - 18\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-8a-15\right){x}-22a-18$ |
| 5041.1-CMa1 |
5041.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5041.1 |
\( 71^{2} \) |
\( 71^{6} \) |
$1.99213$ |
$(-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$71$ |
71Cs.2.1 |
$9$ |
\( 2^{2} \) |
$1$ |
$1.552539401$ |
2.640621315 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -10 a + 23\) , \( 24 a + 24\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-10a+23\right){x}+24a+24$ |
| 5041.3-CMa1 |
5041.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5041.3 |
\( 71^{2} \) |
\( 71^{6} \) |
$1.99213$ |
$(2a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$71$ |
71Cs.2.1 |
$9$ |
\( 2^{2} \) |
$1$ |
$1.552539401$ |
2.640621315 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 10 a + 13\) , \( -24 a + 48\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(10a+13\right){x}-24a+48$ |
| 5184.1-CMa1 |
5184.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5184.1 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{12} \) |
$2.00611$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.541720180$ |
1.165430910 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 15 a + 6\) , \( -8 a - 48\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(15a+6\right){x}-8a-48$ |
| 5184.7-CMa1 |
5184.7-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5184.7 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{12} \) |
$2.00611$ |
$(-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.541720180$ |
1.165430910 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -15 a + 20\) , \( -7 a - 36\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-15a+20\right){x}-7a-36$ |
| 6241.1-CMa1 |
6241.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6241.1 |
\( 79^{2} \) |
\( 79^{6} \) |
$2.10136$ |
$(-6a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$79$ |
79Cs.2.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.471832063$ |
0.278150115 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -15 a - 7\) , \( 47 a - 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-15a-7\right){x}+47a-10$ |
| 6241.3-CMa1 |
6241.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6241.3 |
\( 79^{2} \) |
\( 79^{6} \) |
$2.10136$ |
$(6a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$79$ |
79Cs.2.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.471832063$ |
0.278150115 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 15 a - 22\) , \( -47 a + 37\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(15a-22\right){x}-47a+37$ |
| 7744.1-CMa1 |
7744.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.1 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{6} \) |
$2.21783$ |
$(a), (-2a+3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.689550794$ |
$1.394538373$ |
2.907620347 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -15 a + 26\) , \( -8 a - 80\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a+26\right){x}-8a-80$ |
| 7744.19-CMa1 |
7744.19-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.19 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{6} \) |
$2.21783$ |
$(-a+1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.394538373$ |
1.054171922 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -6 a - 23\) , \( 15 a + 46\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-6a-23\right){x}+15a+46$ |
| 7744.21-CMa1 |
7744.21-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.21 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{6} \) |
$2.21783$ |
$(-a+1), (2a+1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.689550794$ |
$1.394538373$ |
2.907620347 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 15 a + 10\) , \( 23 a - 78\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(15a+10\right){x}+23a-78$ |
| 7744.3-CMa1 |
7744.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.3 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{6} \) |
$2.21783$ |
$(a), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.394538373$ |
1.054171922 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 7 a - 28\) , \( -22 a + 91\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a-28\right){x}-22a+91$ |
| 9801.1-CMa1 |
9801.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9801.1 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{6} \) |
$2.35237$ |
$(-2a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.314783387$ |
0.993882820 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -23 a + 3\) , \( -52 a + 58\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-23a+3\right){x}-52a+58$ |
| 9801.3-CMa1 |
9801.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9801.3 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{6} \) |
$2.35237$ |
$(2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.314783387$ |
0.993882820 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 22 a - 20\) , \( 51 a + 6\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(22a-20\right){x}+51a+6$ |
| 10000.1-CMa1 |
10000.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10000.1 |
\( 2^{4} \cdot 5^{4} \) |
\( 2^{12} \cdot 5^{12} \) |
$2.36422$ |
$(a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.308192952$ |
0.988900920 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -23 a + 17\) , \( -22 a + 67\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23a+17\right){x}-22a+67$ |
| 10000.5-CMa1 |
10000.5-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10000.5 |
\( 2^{4} \cdot 5^{4} \) |
\( 2^{12} \cdot 5^{12} \) |
$2.36422$ |
$(-a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.308192952$ |
0.988900920 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 24 a - 8\) , \( 45 a + 37\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(24a-8\right){x}+45a+37$ |
| 11449.1-CMa1 |
11449.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11449.1 |
\( 107^{2} \) |
\( 107^{6} \) |
$2.44557$ |
$(-2a+11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$107$ |
107Cs.3.1 |
$9$ |
\( 2^{2} \) |
$1$ |
$1.264677862$ |
2.151014857 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -13 a + 35\) , \( -47 a - 48\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-13a+35\right){x}-47a-48$ |
| 11449.3-CMa1 |
11449.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11449.3 |
\( 107^{2} \) |
\( 107^{6} \) |
$2.44557$ |
$(2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$107$ |
107Cs.3.1 |
$9$ |
\( 2^{2} \) |
$1$ |
$1.264677862$ |
2.151014857 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 12 a + 23\) , \( 46 a - 94\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(12a+23\right){x}+46a-94$ |
| 12544.5-CMa1 |
12544.5-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12544.5 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{6} \) |
$2.50205$ |
$(a), (-a+1), (-2a+1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{6} \) |
$0.325958851$ |
$1.236126150$ |
4.873337972 |
\( -3375 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -35\) , \( 98\bigr] \) |
${y}^2={x}^{3}-35{x}+98$ |
| 13456.1-CMa1 |
13456.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13456.1 |
\( 2^{4} \cdot 29^{2} \) |
\( 2^{12} \cdot 29^{6} \) |
$2.54634$ |
$(a), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$4$ |
\( 2^{4} \) |
$1$ |
$1.214626663$ |
3.672685815 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 27 a - 3\) , \( 12 a + 95\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(27a-3\right){x}+12a+95$ |
| 13456.13-CMa1 |
13456.13-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13456.13 |
\( 2^{4} \cdot 29^{2} \) |
\( 2^{12} \cdot 29^{6} \) |
$2.54634$ |
$(-a+1), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.214626663$ |
0.918171453 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -25 a - 5\) , \( 64 a - 32\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-25a-5\right){x}+64a-32$ |
| 13456.15-CMa1 |
13456.15-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13456.15 |
\( 2^{4} \cdot 29^{2} \) |
\( 2^{12} \cdot 29^{6} \) |
$2.54634$ |
$(-a+1), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$4$ |
\( 2^{4} \) |
$1$ |
$1.214626663$ |
3.672685815 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -26 a + 22\) , \( -39 a + 129\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-26a+22\right){x}-39a+129$ |
| 13456.3-CMa1 |
13456.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13456.3 |
\( 2^{4} \cdot 29^{2} \) |
\( 2^{12} \cdot 29^{6} \) |
$2.54634$ |
$(a), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.214626663$ |
0.918171453 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 25 a - 29\) , \( -89 a + 62\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(25a-29\right){x}-89a+62$ |
| 16129.1-CMa1 |
16129.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16129.1 |
\( 127^{2} \) |
\( 127^{6} \) |
$2.66434$ |
$(-6a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$127$ |
127Cs.9.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.160833532$ |
0.219376917 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 30 a - 15\) , \( -70 a - 50\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(30a-15\right){x}-70a-50$ |
| 16129.3-CMa1 |
16129.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16129.3 |
\( 127^{2} \) |
\( 127^{6} \) |
$2.66434$ |
$(6a-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$127$ |
127Cs.9.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.160833532$ |
0.219376917 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -30 a + 15\) , \( 70 a - 120\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-30a+15\right){x}+70a-120$ |
| 21904.1-CMa1 |
21904.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21904.1 |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{6} \) |
$2.87620$ |
$(a), (-4a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.075327983$ |
0.812871549 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 15 a - 49\) , \( 67 a - 122\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(15a-49\right){x}+67a-122$ |
| 21904.13-CMa1 |
21904.13-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21904.13 |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{6} \) |
$2.87620$ |
$(-a+1), (-4a+5)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$2.176176600$ |
$1.075327983$ |
7.075808175 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -21 a + 47\) , \( -60 a - 72\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-21a+47\right){x}-60a-72$ |
| 21904.15-CMa1 |
21904.15-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21904.15 |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{6} \) |
$2.87620$ |
$(-a+1), (4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$1.075327983$ |
0.812871549 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -15 a - 35\) , \( -82 a - 90\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-15a-35\right){x}-82a-90$ |
| 21904.3-CMa1 |
21904.3-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21904.3 |
\( 2^{4} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{6} \) |
$2.87620$ |
$(a), (4a+1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$2.176176600$ |
$1.075327983$ |
7.075808175 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 22 a + 27\) , \( 38 a - 157\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(22a+27\right){x}+38a-157$ |
| 22801.1-CMa1 |
22801.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
22801.1 |
\( 151^{2} \) |
\( 151^{6} \) |
$2.90520$ |
$(-2a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$151$ |
151Cs.5.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.064592326$ |
0.201189038 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -15 a + 50\) , \( 96 a + 34\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-15a+50\right){x}+96a+34$ |
*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.
