| 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 |
$8$ |
$42$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-84$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$365.3998120$ |
1.087499440 |
\( 159348833280 a^{3} + 348799965696 a^{2} - 33256065024 a - 72799677504 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - 4 a\) , \( -5 a^{3} + 10 a^{2} + 9 a - 4\) , \( -70 a^{3} + 156 a^{2} + 13 a - 33\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-5a^{3}+10a^{2}+9a-4\right){x}-70a^{3}+156a^{2}+13a-33$ |
| 1.1-a2 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-84$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$365.3998120$ |
1.087499440 |
\( -763488101376 a^{3} - 348799965696 a^{2} + 3658091673600 a + 1671200150976 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - 4 a\) , \( 44 a^{3} - 88 a^{2} - 19 a + 13\) , \( 467 a^{3} - 1040 a^{2} - 63 a + 232\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(44a^{3}-88a^{2}-19a+13\right){x}+467a^{3}-1040a^{2}-63a+232$ |
| 1.1-a3 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-84$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$365.3998120$ |
1.087499440 |
\( -159348833280 a^{3} + 348799965696 a^{2} + 33256065024 a - 72799677504 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 1\) , \( 4 a^{3} + 10 a^{2} + a - 3\) , \( 76 a^{3} + 170 a^{2} - 7 a - 33\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+{y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(4a^{3}+10a^{2}+a-3\right){x}+76a^{3}+170a^{2}-7a-33$ |
| 1.1-a4 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-84$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$365.3998120$ |
1.087499440 |
\( 763488101376 a^{3} - 348799965696 a^{2} - 3658091673600 a + 1671200150976 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 1\) , \( -45 a^{3} - 88 a^{2} + 29 a + 14\) , \( -542 a^{3} - 1194 a^{2} + 99 a + 253\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+{y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-45a^{3}-88a^{2}+29a+14\right){x}-542a^{3}-1194a^{2}+99a+253$ |
| 1.1-a5 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-84$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$365.3998120$ |
1.087499440 |
\( -159348833280 a^{3} + 348799965696 a^{2} + 33256065024 a - 72799677504 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 4 a\) , \( 7 a^{3} + 8 a^{2} - 17 a + 1\) , \( -64 a^{3} - 147 a^{2} + 31\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(7a^{3}+8a^{2}-17a+1\right){x}-64a^{3}-147a^{2}+31$ |
| 1.1-a6 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-84$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$365.3998120$ |
1.087499440 |
\( 763488101376 a^{3} - 348799965696 a^{2} - 3658091673600 a + 1671200150976 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 4 a\) , \( -42 a^{3} - 90 a^{2} + 11 a + 18\) , \( 424 a^{3} + 951 a^{2} - 48 a - 217\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(-42a^{3}-90a^{2}+11a+18\right){x}+424a^{3}+951a^{2}-48a-217$ |
| 1.1-a7 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-84$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$365.3998120$ |
1.087499440 |
\( 159348833280 a^{3} + 348799965696 a^{2} - 33256065024 a - 72799677504 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( 1\) , \( -2 a^{3} + 8 a^{2} - 9 a + 2\) , \( 73 a^{3} - 161 a^{2} - 12 a + 32\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(-2a^{3}+8a^{2}-9a+2\right){x}+73a^{3}-161a^{2}-12a+32$ |
| 1.1-a8 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-84$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$365.3998120$ |
1.087499440 |
\( -763488101376 a^{3} - 348799965696 a^{2} + 3658091673600 a + 1671200150976 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( 1\) , \( 47 a^{3} - 90 a^{2} - 37 a + 19\) , \( -496 a^{3} + 1105 a^{2} + 66 a - 237\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(47a^{3}-90a^{2}-37a+19\right){x}-496a^{3}+1105a^{2}+66a-237$ |
| 1.1-b1 |
1.1-b |
$8$ |
$28$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$42.78422004$ |
0.509335952 |
\( -51954490735875 a^{3} + 311726944415250 a + 137458661985000 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a^{2} - a + 2\) , \( a^{2} + a - 3\) , \( -79 a^{3} - 121 a^{2} + 109 a - 10\) , \( -655 a^{3} - 1532 a^{2} - 36 a + 392\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-79a^{3}-121a^{2}+109a-10\right){x}-655a^{3}-1532a^{2}-36a+392$ |
| 1.1-b2 |
1.1-b |
$8$ |
$28$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.509335952 |
\( 16581375 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a^{2} - a + 2\) , \( 1\) , \( 17 a^{3} - 2 a^{2} - 63 a - 25\) , \( -5 a^{3} - 37 a^{2} + 83 a + 45\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(17a^{3}-2a^{2}-63a-25\right){x}-5a^{3}-37a^{2}+83a+45$ |
| 1.1-b3 |
1.1-b |
$8$ |
$28$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$42.78422004$ |
0.509335952 |
\( 51954490735875 a^{3} - 311726944415250 a + 137458661985000 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a^{2} - a + 2\) , \( 1\) , \( 72 a^{3} - 122 a^{2} - 73 a - 5\) , \( 784 a^{3} - 1742 a^{2} - 116 a + 375\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(72a^{3}-122a^{2}-73a-5\right){x}+784a^{3}-1742a^{2}-116a+375$ |
| 1.1-b4 |
1.1-b |
$8$ |
$28$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.509335952 |
\( -3375 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a^{2} - a + 2\) , \( 1\) , \( -3 a^{3} - 2 a^{2} + 17 a + 10\) , \( -2 a^{3} - 2 a^{2} + 10 a + 5\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-3a^{3}-2a^{2}+17a+10\right){x}-2a^{3}-2a^{2}+10a+5$ |
| 1.1-b5 |
1.1-b |
$8$ |
$28$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.509335952 |
\( 16581375 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( 21 a^{3} + a^{2} - 81 a - 35\) , \( 25 a^{3} + 37 a^{2} - 159 a - 78\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-5a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(21a^{3}+a^{2}-81a-35\right){x}+25a^{3}+37a^{2}-159a-78$ |
| 1.1-b6 |
1.1-b |
$8$ |
$28$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.509335952 |
\( 51954490735875 a^{3} - 311726944415250 a + 137458661985000 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( 76 a^{3} - 119 a^{2} - 91 a - 15\) , \( -709 a^{3} + 1622 a^{2} + 30 a - 388\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-5a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(76a^{3}-119a^{2}-91a-15\right){x}-709a^{3}+1622a^{2}+30a-388$ |
| 1.1-b7 |
1.1-b |
$8$ |
$28$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.509335952 |
\( -3375 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} + a^{2} - a\) , \( 2 a^{3} + 2 a^{2} - 6 a - 3\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-5a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(a^{3}+a^{2}-a\right){x}+2a^{3}+2a^{2}-6a-3$ |
| 1.1-b8 |
1.1-b |
$8$ |
$28$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50616$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$684.5475207$ |
0.509335952 |
\( -51954490735875 a^{3} + 311726944415250 a + 137458661985000 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 1\) , \( -77 a^{3} - 119 a^{2} + 102 a - 13\) , \( 576 a^{3} + 1412 a^{2} + 146 a - 405\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+{y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(-77a^{3}-119a^{2}+102a-13\right){x}+576a^{3}+1412a^{2}+146a-405$ |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$9.87866$ |
$(-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$3458.948137$ |
2.287664112 |
\( -7171072 a^{3} + 15855424 a^{2} + 1482368 a - 3302976 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 6 a + 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 5 a^{3} - 3 a^{2} - 27 a + 9\) , \( 4 a^{3} - 17 a + 5\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+4\right){x}^{2}+\left(5a^{3}-3a^{2}-27a+9\right){x}+4a^{3}-17a+5$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$9.87866$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$384.3275708$ |
2.287664112 |
\( -16256 a^{3} + 31680 a^{2} + 9600 a - 2048 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - a^{2} - 5 a + 3\) , \( a^{3} - 5 a + 1\) , \( -2 a^{3} + 10 a - 1\) , \( -5 a^{3} + 2 a^{2} + 24 a - 10\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+3\right){x}^{2}+\left(-2a^{3}+10a-1\right){x}-5a^{3}+2a^{2}+24a-10$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$9.87866$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$384.3275708$ |
2.287664112 |
\( 71680 a^{3} - 31680 a^{2} - 342144 a + 156352 \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 2\) , \( a + 1\) , \( -a^{2} + a + 2\) , \( a^{3} - 2 a^{2} - a\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-a^{2}+a+2\right){x}+a^{3}-2a^{2}-a$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$9.87866$ |
$(-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$3458.948137$ |
2.287664112 |
\( 34372992 a^{3} - 15855424 a^{2} - 164693888 a + 75974144 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{2} + a - 4\) , \( a\) , \( 2 a^{3} - 8 a - 1\) , \( -4 a^{3} - a^{2} + 19 a + 8\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(2a^{3}-8a-1\right){x}-4a^{3}-a^{2}+19a+8$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$9.87866$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.046528784$ |
$873.2894869$ |
1.934909428 |
\( 1728 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 6 a + 1\) , \( a^{3} - 4 a\) , \( -8 a^{3} + 20 a^{2} - 5 a - 3\) , \( -18 a^{3} + 40 a^{2} + 2 a - 8\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-6a+1\right){x}^{2}+\left(-8a^{3}+20a^{2}-5a-3\right){x}-18a^{3}+40a^{2}+2a-8$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$9.87866$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.093057568$ |
$873.2894869$ |
1.934909428 |
\( 1728 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 6 a + 1\) , \( 1\) , \( -a^{2} + 4\) , \( a^{3} - 2 a^{2} - a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-6a+1\right){x}^{2}+\left(-a^{2}+4\right){x}+a^{3}-2a^{2}-a+1$ |
| 9.1-c1 |
9.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$9.87866$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$168.5501065$ |
1.003274443 |
\( -7171072 a^{3} + 15855424 a^{2} + 1482368 a - 3302976 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{2} - 2\) , \( -2 a^{3} - a^{2} + 7 a + 2\) , \( -a^{3} - a^{2} + a - 5\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(-2a^{3}-a^{2}+7a+2\right){x}-a^{3}-a^{2}+a-5$ |
| 9.1-c2 |
9.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$9.87866$ |
$(-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1516.950959$ |
1.003274443 |
\( -16256 a^{3} + 31680 a^{2} + 9600 a - 2048 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( a^{3} + a^{2} - 4 a - 4\) , \( a\) , \( -3 a^{3} + 2 a^{2} + 14 a - 6\) , \( 2 a^{3} - a^{2} - 9 a + 5\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-4a-4\right){x}^{2}+\left(-3a^{3}+2a^{2}+14a-6\right){x}+2a^{3}-a^{2}-9a+5$ |
| 9.1-c3 |
9.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$9.87866$ |
$(-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1516.950959$ |
1.003274443 |
\( 71680 a^{3} - 31680 a^{2} - 342144 a + 156352 \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} - 4 a^{2} + 6 a + 9\) , \( -a^{3} - 2 a^{2} + 5 a + 6\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+4\right){x}^{2}+\left(-a^{3}-4a^{2}+6a+9\right){x}-a^{3}-2a^{2}+5a+6$ |
| 9.1-c4 |
9.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$9.87866$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$168.5501065$ |
1.003274443 |
\( 34372992 a^{3} - 15855424 a^{2} - 164693888 a + 75974144 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} - a^{2} + 6 a + 2\) , \( a\) , \( -2 a\) , \( 4 a^{3} + a^{2} - 20 a - 9\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}-a^{2}+6a+2\right){x}^{2}-2a{x}+4a^{3}+a^{2}-20a-9$ |
| 9.2-a1 |
9.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{3} \) |
$9.87866$ |
$(-a^3+5a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$3458.948137$ |
2.287664112 |
\( 7171072 a^{3} + 15855424 a^{2} - 1482368 a - 3302976 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 5 a + 4\) , \( a + 1\) , \( 5 a^{3} - 3 a^{2} - 23 a + 8\) , \( 3 a^{3} - a^{2} - 17 a + 8\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+4\right){x}^{2}+\left(5a^{3}-3a^{2}-23a+8\right){x}+3a^{3}-a^{2}-17a+8$ |
| 9.2-a2 |
9.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$9.87866$ |
$(-a^3+5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$384.3275708$ |
2.287664112 |
\( 16256 a^{3} + 31680 a^{2} - 9600 a - 2048 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 5 a + 1\) , \( 3 a^{3} - 14 a - 1\) , \( 4 a^{3} + 2 a^{2} - 19 a - 10\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(3a^{3}-14a-1\right){x}+4a^{3}+2a^{2}-19a-10$ |
| 9.2-a3 |
9.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$9.87866$ |
$(-a^3+5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$384.3275708$ |
2.287664112 |
\( -71680 a^{3} - 31680 a^{2} + 342144 a + 156352 \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a + 1\) , \( -a^{3} - a^{2} + a + 2\) , \( -a^{3} - 2 a^{2}\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-a^{3}-a^{2}+a+2\right){x}-a^{3}-2a^{2}$ |
| 9.2-a4 |
9.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{3} \) |
$9.87866$ |
$(-a^3+5a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$3458.948137$ |
2.287664112 |
\( -34372992 a^{3} - 15855424 a^{2} + 164693888 a + 75974144 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + a^{2} + 6 a - 4\) , \( a^{2} - 3\) , \( a^{3} - 4 a + 1\) , \( 4 a^{3} - a^{2} - 20 a + 7\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-4\right){x}^{2}+\left(a^{3}-4a+1\right){x}+4a^{3}-a^{2}-20a+7$ |
| 9.2-b1 |
9.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$9.87866$ |
$(-a^3+5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.093057568$ |
$873.2894869$ |
1.934909428 |
\( 1728 \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 6 a + 1\) , \( a^{3} - 4 a\) , \( 7 a^{3} - 35 a + 1\) , \( 2 a^{3} - a^{2} - 10 a + 5\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-6a+1\right){x}^{2}+\left(7a^{3}-35a+1\right){x}+2a^{3}-a^{2}-10a+5$ |
| 9.2-b2 |
9.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$9.87866$ |
$(-a^3+5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.046528784$ |
$873.2894869$ |
1.934909428 |
\( 1728 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 6 a + 1\) , \( 1\) , \( 8 a^{3} + 19 a^{2} - 2 a\) , \( -a^{3} - a^{2} - a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-6a+1\right){x}^{2}+\left(8a^{3}+19a^{2}-2a\right){x}-a^{3}-a^{2}-a+1$ |
| 9.2-c1 |
9.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{3} \) |
$9.87866$ |
$(-a^3+5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$168.5501065$ |
1.003274443 |
\( 7171072 a^{3} + 15855424 a^{2} - 1482368 a - 3302976 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 6 a - 3\) , \( a^{3} - 5 a\) , \( -2 a^{3} + 10 a\) , \( -a^{2} + 4 a - 4\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-3\right){x}^{2}+\left(-2a^{3}+10a\right){x}-a^{2}+4a-4$ |
| 9.2-c2 |
9.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$9.87866$ |
$(-a^3+5a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1516.950959$ |
1.003274443 |
\( 16256 a^{3} + 31680 a^{2} - 9600 a - 2048 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a\) , \( 2 a^{3} + 2 a^{2} - 12 a - 6\) , \( -2 a^{3} - a^{2} + 9 a + 5\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(2a^{3}+2a^{2}-12a-6\right){x}-2a^{3}-a^{2}+9a+5$ |
| 9.2-c3 |
9.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$9.87866$ |
$(-a^3+5a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1516.950959$ |
1.003274443 |
\( -71680 a^{3} - 31680 a^{2} + 342144 a + 156352 \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 2 a^{3} - 4 a^{2} - 14 a + 9\) , \( 3 a^{3} - 2 a^{2} - 16 a + 6\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(2a^{3}-4a^{2}-14a+9\right){x}+3a^{3}-2a^{2}-16a+6$ |
| 9.2-c4 |
9.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{3} \) |
$9.87866$ |
$(-a^3+5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$168.5501065$ |
1.003274443 |
\( -34372992 a^{3} - 15855424 a^{2} + 164693888 a + 75974144 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 3\) , \( -a^{3} + 2 a\) , \( -4 a^{3} + a^{2} + 19 a - 10\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-a^{3}+2a\right){x}-4a^{3}+a^{2}+19a-10$ |
| 9.3-a1 |
9.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{14} \) |
$9.87866$ |
$(-a-1), (-a^3+5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.232242074$ |
$131.1093345$ |
1.449957322 |
\( \frac{968192}{729} a^{3} - \frac{1936384}{243} a + \frac{2296256}{729} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 4 a + 1\) , \( 1\) , \( -2 a^{2} + 4 a + 4\) , \( a^{3} - 3 a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(-2a^{2}+4a+4\right){x}+a^{3}-3a^{2}+a+1$ |
| 9.3-a2 |
9.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{10} \) |
$9.87866$ |
$(-a-1), (-a^3+5a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.077414024$ |
$1179.984011$ |
1.449957322 |
\( \frac{4301312}{27} a^{3} - \frac{8602624}{9} a + \frac{11388736}{27} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( 1\) , \( -22 a^{3} + 11 a^{2} + 106 a - 47\) , \( 98 a^{3} - 43 a^{2} - 467 a + 213\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-22a^{3}+11a^{2}+106a-47\right){x}+98a^{3}-43a^{2}-467a+213$ |
| 9.3-a3 |
9.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{14} \) |
$9.87866$ |
$(-a-1), (-a^3+5a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.038707012$ |
$1179.984011$ |
1.449957322 |
\( -\frac{968192}{729} a^{3} + \frac{1936384}{243} a + \frac{2296256}{729} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + 4 a + 1\) , \( a^{3} - 4 a\) , \( 3 a^{3} + a^{2} - 15 a - 4\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(3a^{3}+a^{2}-15a-4\right){x}$ |
| 9.3-a4 |
9.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{10} \) |
$9.87866$ |
$(-a-1), (-a^3+5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$0.116121037$ |
$131.1093345$ |
1.449957322 |
\( -\frac{4301312}{27} a^{3} + \frac{8602624}{9} a + \frac{11388736}{27} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 22 a^{3} + 10 a^{2} - 107 a - 47\) , \( 121 a^{3} + 54 a^{2} - 578 a - 263\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(22a^{3}+10a^{2}-107a-47\right){x}+121a^{3}+54a^{2}-578a-263$ |
| 9.3-b1 |
9.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{14} \) |
$9.87866$ |
$(-a-1), (-a^3+5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.232242074$ |
$131.1093345$ |
1.449957322 |
\( -\frac{968192}{729} a^{3} + \frac{1936384}{243} a + \frac{2296256}{729} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 5 a + 1\) , \( 1\) , \( -a^{3} - 2 a^{2} + a + 4\) , \( -a^{3} - 3 a^{2} - a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-a^{3}-2a^{2}+a+4\right){x}-a^{3}-3a^{2}-a+1$ |
| 9.3-b2 |
9.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{10} \) |
$9.87866$ |
$(-a-1), (-a^3+5a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.077414024$ |
$1179.984011$ |
1.449957322 |
\( -\frac{4301312}{27} a^{3} + \frac{8602624}{9} a + \frac{11388736}{27} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 3\) , \( 1\) , \( 22 a^{3} + 11 a^{2} - 107 a - 47\) , \( -98 a^{3} - 43 a^{2} + 467 a + 213\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(22a^{3}+11a^{2}-107a-47\right){x}-98a^{3}-43a^{2}+467a+213$ |
| 9.3-b3 |
9.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{14} \) |
$9.87866$ |
$(-a-1), (-a^3+5a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.038707012$ |
$1179.984011$ |
1.449957322 |
\( \frac{968192}{729} a^{3} - \frac{1936384}{243} a + \frac{2296256}{729} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 5 a + 1\) , \( a^{3} - 4 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(a^{3}-a^{2}-4a+1\right){x}$ |
| 9.3-b4 |
9.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{10} \) |
$9.87866$ |
$(-a-1), (-a^3+5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$0.116121037$ |
$131.1093345$ |
1.449957322 |
\( \frac{4301312}{27} a^{3} - \frac{8602624}{9} a + \frac{11388736}{27} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -20 a^{3} + 10 a^{2} + 96 a - 47\) , \( -118 a^{3} + 54 a^{2} + 564 a - 263\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-20a^{3}+10a^{2}+96a-47\right){x}-118a^{3}+54a^{2}+564a-263$ |
| 12.1-a1 |
12.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$10.24037$ |
$(-a-1), (a^3-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$37.07206165$ |
2.648004403 |
\( -\frac{1500083}{72} a^{3} + \frac{1500083}{12} a - \frac{495212}{9} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 5 a - 1\) , \( a\) , \( -3 a^{3} - 3 a^{2} + 16 a + 9\) , \( 22 a^{3} + 8 a^{2} - 102 a - 47\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(-3a^{3}-3a^{2}+16a+9\right){x}+22a^{3}+8a^{2}-102a-47$ |
| 12.1-a2 |
12.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{12} \) |
$10.24037$ |
$(-a-1), (a^3-4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$333.6485548$ |
2.648004403 |
\( \frac{275587}{1458} a^{3} - \frac{275587}{243} a + \frac{289048}{729} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( a^{2} - 2\) , \( 3 a^{3} - 14 a\) , \( -5 a^{3} - 2 a^{2} + 24 a + 8\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-3\right){x}^{2}+\left(3a^{3}-14a\right){x}-5a^{3}-2a^{2}+24a+8$ |
| 12.1-a3 |
12.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{24} \) |
$10.24037$ |
$(-a-1), (a^3-4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$333.6485548$ |
2.648004403 |
\( -\frac{62446099201}{1062882} a^{3} + \frac{62446099201}{177147} a + \frac{168555918709}{1062882} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( a^{2} - 2\) , \( 33 a^{3} + 15 a^{2} - 159 a - 75\) , \( -155 a^{3} - 71 a^{2} + 743 a + 339\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-3\right){x}^{2}+\left(33a^{3}+15a^{2}-159a-75\right){x}-155a^{3}-71a^{2}+743a+339$ |
| 12.1-a4 |
12.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$10.24037$ |
$(-a-1), (a^3-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$37.07206165$ |
2.648004403 |
\( \frac{752904308551}{324} a^{3} - \frac{752904308551}{54} a + \frac{1992001566899}{324} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 5 a - 1\) , \( a\) , \( 57 a^{3} + 7 a^{2} - 234 a - 121\) , \( 292 a^{3} + 26 a^{2} - 1192 a - 579\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(57a^{3}+7a^{2}-234a-121\right){x}+292a^{3}+26a^{2}-1192a-579$ |
| 12.1-b1 |
12.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$10.24037$ |
$(-a-1), (a^3-4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.084709236$ |
$1124.524693$ |
1.512025852 |
\( -\frac{1500083}{72} a^{3} + \frac{1500083}{12} a - \frac{495212}{9} \) |
\( \bigl[a\) , \( -a^{3} + 5 a - 1\) , \( a^{2} - 3\) , \( -3 a^{3} - 3 a^{2} + 16 a + 9\) , \( -22 a^{3} - 8 a^{2} + 102 a + 45\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+5a-1\right){x}^{2}+\left(-3a^{3}-3a^{2}+16a+9\right){x}-22a^{3}-8a^{2}+102a+45$ |
| 12.1-b2 |
12.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{3}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{12} \) |
$10.24037$ |
$(-a-1), (a^3-4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.254127710$ |
$124.9471882$ |
1.512025852 |
\( \frac{275587}{1458} a^{3} - \frac{275587}{243} a + \frac{289048}{729} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - a^{2} - 6 a + 3\) , \( a^{2} + a - 2\) , \( 3 a^{3} - 2 a^{2} - 17 a + 4\) , \( 7 a^{3} + a^{2} - 35 a - 8\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+3\right){x}^{2}+\left(3a^{3}-2a^{2}-17a+4\right){x}+7a^{3}+a^{2}-35a-8$ |
*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.
