| 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 |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-288$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
0.372767982 |
\( 10657126796357691195000 a^{3} + 20587988013278347844000 a^{2} - 2855568518720121841000 a - 5516534761939567995000 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - a - 1\) , \( a^{3} - 3 a + 1\) , \( 5 a^{3} + 3 a^{2} - 40 a - 41\) , \( -23 a^{3} + 8 a^{2} + 135 a + 72\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(5a^{3}+3a^{2}-40a-41\right){x}-23a^{3}+8a^{2}+135a+72$ |
| 1.1-a2 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-288$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
0.372767982 |
\( -10657126796357691195000 a^{3} + 20587988013278347844000 a^{2} + 2855568518720121841000 a - 5516534761939567995000 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} - 2\) , \( -7 a^{3} + 2 a^{2} + 42 a - 39\) , \( 60 a^{3} - 15 a^{2} - 251 a + 108\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-7a^{3}+2a^{2}+42a-39\right){x}+60a^{3}-15a^{2}-251a+108$ |
| 1.1-a3 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-288$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
0.372767982 |
\( -39772938666710642939000 a^{3} - 20587988013278347844000 a^{2} + 148434627870484880561000 a + 76835417291173823381000 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 3 a + 1\) , \( 20 a^{3} - 4 a^{2} - 86 a - 27\) , \( -44 a^{3} - 8 a^{2} + 198 a + 104\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(20a^{3}-4a^{2}-86a-27\right){x}-44a^{3}-8a^{2}+198a+104$ |
| 1.1-a4 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
0.372767982 |
\( -18473000 a^{3} + 55419000 a + 26125000 \) |
\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 5 a - 2\) , \( -a^{3} + 4 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+2\right){x}^{2}+\left(a^{3}+a^{2}-5a-2\right){x}-a^{3}+4a-1$ |
| 1.1-a5 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-288$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
0.372767982 |
\( 39772938666710642939000 a^{3} - 20587988013278347844000 a^{2} - 148434627870484880561000 a + 76835417291173823381000 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{2} - 2\) , \( -14 a^{3} - 2 a^{2} + 63 a - 31\) , \( 11 a^{3} + 15 a^{2} - 104 a + 48\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(-14a^{3}-2a^{2}+63a-31\right){x}+11a^{3}+15a^{2}-104a+48$ |
| 1.1-a6 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
0.372767982 |
\( 18473000 a^{3} - 55419000 a + 26125000 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{2} - 2\) , \( a^{3} - 2 a^{2} - 7 a + 4\) , \( -a^{3} - 5 a^{2} - 4 a + 3\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(a^{3}-2a^{2}-7a+4\right){x}-a^{3}-5a^{2}-4a+3$ |
| 1.1-a7 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2576.572294$ |
0.372767982 |
\( 77092288000 a^{3} - 385461440000 a + 188837384000 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a - 1\) , \( 1\) , \( 15 a^{3} - 76 a - 40\) , \( -73 a^{3} + 365 a + 179\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(15a^{3}-76a-40\right){x}-73a^{3}+365a+179$ |
| 1.1-a8 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2576.572294$ |
0.372767982 |
\( 8000 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a - 1\) , \( 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}-a{x}$ |
| 1.1-a9 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$31.80953449$ |
0.372767982 |
\( -77092288000 a^{3} + 385461440000 a + 188837384000 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a\) , \( a^{2} - 2\) , \( -15 a^{3} + 75 a - 40\) , \( -73 a^{3} + 365 a - 180\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-15a^{3}+75a-40\right){x}-73a^{3}+365a-180$ |
| 1.1-a10 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2576.572294$ |
0.372767982 |
\( -77092288000 a^{3} + 385461440000 a + 188837384000 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a - 1\) , \( 1\) , \( -16 a^{3} + 79 a - 40\) , \( 73 a^{3} - 365 a + 179\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+5a-1\right){x}^{2}+\left(-16a^{3}+79a-40\right){x}+73a^{3}-365a+179$ |
| 1.1-a11 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$31.80953449$ |
0.372767982 |
\( 77092288000 a^{3} - 385461440000 a + 188837384000 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a\) , \( a^{2} - 2\) , \( 16 a^{3} - 80 a - 40\) , \( 73 a^{3} - 365 a - 180\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(16a^{3}-80a-40\right){x}+73a^{3}-365a-180$ |
| 1.1-a12 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2576.572294$ |
0.372767982 |
\( 8000 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a\) , \( a^{2} - 2\) , \( a^{3} - 5 a\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(a^{3}-5a\right){x}-1$ |
| 1.1-a13 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-288$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$7.952383624$ |
0.372767982 |
\( -39772938666710642939000 a^{3} - 20587988013278347844000 a^{2} + 148434627870484880561000 a + 76835417291173823381000 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 3 a + 1\) , \( 14 a^{3} - a^{2} - 65 a - 33\) , \( 27 a^{3} - 10 a^{2} - 136 a - 66\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(14a^{3}-a^{2}-65a-33\right){x}+27a^{3}-10a^{2}-136a-66$ |
| 1.1-a14 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
0.372767982 |
\( -18473000 a^{3} + 55419000 a + 26125000 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} - 2\) , \( 3 a^{3} + 2 a^{2} - 13 a - 4\) , \( 8 a^{3} + 5 a^{2} - 31 a - 17\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(3a^{3}+2a^{2}-13a-4\right){x}+8a^{3}+5a^{2}-31a-17$ |
| 1.1-a15 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-288$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$7.952383624$ |
0.372767982 |
\( 39772938666710642939000 a^{3} - 20587988013278347844000 a^{2} - 148434627870484880561000 a + 76835417291173823381000 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 1\) , \( -16 a^{3} - 2 a^{2} + 71 a - 32\) , \( -62 a^{3} + 5 a^{2} + 275 a - 136\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(-16a^{3}-2a^{2}+71a-32\right){x}-62a^{3}+5a^{2}+275a-136$ |
| 1.1-a16 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
0.372767982 |
\( 18473000 a^{3} - 55419000 a + 26125000 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 1\) , \( -a^{3} - 2 a^{2} + a + 3\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(-a^{3}-2a^{2}+a+3\right){x}-1$ |
| 1.1-a17 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-288$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$7.952383624$ |
0.372767982 |
\( 10657126796357691195000 a^{3} + 20587988013278347844000 a^{2} - 2855568518720121841000 a - 5516534761939567995000 \) |
\( \bigl[a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 6 a^{3} + a^{2} - 42 a - 38\) , \( 29 a^{3} - 6 a^{2} - 177 a - 114\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(6a^{3}+a^{2}-42a-38\right){x}+29a^{3}-6a^{2}-177a-114$ |
| 1.1-a18 |
1.1-a |
$18$ |
$72$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.28923$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-288$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$7.952383624$ |
0.372767982 |
\( -10657126796357691195000 a^{3} + 20587988013278347844000 a^{2} + 2855568518720121841000 a - 5516534761939567995000 \) |
\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a^{3} - 3 a + 1\) , \( -9 a^{3} + a^{2} + 50 a - 37\) , \( -28 a^{3} + 10 a^{2} + 139 a - 106\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+2\right){x}^{2}+\left(-9a^{3}+a^{2}+50a-37\right){x}-28a^{3}+10a^{2}+139a-106$ |
| 9.1-a1 |
9.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$285.8329267$ |
1.488713160 |
\( -\frac{320418987231990328}{27} a^{3} + \frac{1602094936159951640}{27} a + 29069000837710152 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a\) , \( a\) , \( -2463 a^{3} + 1265 a^{2} + 9170 a - 4780\) , \( 84852 a^{3} - 43876 a^{2} - 316598 a + 163923\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2463a^{3}+1265a^{2}+9170a-4780\right){x}+84852a^{3}-43876a^{2}-316598a+163923$ |
| 9.1-a2 |
9.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$285.8329267$ |
1.488713160 |
\( \frac{467951528}{3} a^{3} - \frac{2339757640}{3} a + 382083912 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -2 a^{3} + a^{2} + 4 a - 14\) , \( -6 a^{3} + 2 a^{2} + 24 a - 7\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-2a^{3}+a^{2}+4a-14\right){x}-6a^{3}+2a^{2}+24a-7$ |
| 9.1-a3 |
9.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$571.6658535$ |
1.488713160 |
\( \frac{58591911104}{243} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -161 a^{3} + 482 a - 243\) , \( 1495 a^{3} - 4486 a + 2128\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(-161a^{3}+482a-243\right){x}+1495a^{3}-4486a+2128$ |
| 9.1-a4 |
9.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$571.6658535$ |
1.488713160 |
\( \frac{85184}{3} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + 2 a - 3\) , \( -a - 2\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(-a^{3}+2a-3\right){x}-a-2$ |
| 9.1-a5 |
9.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$142.9164633$ |
1.488713160 |
\( \frac{64}{9} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - 4 a\) , \( -a - 2\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(a^{3}-4a\right){x}-a-2$ |
| 9.1-a6 |
9.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{40} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$142.9164633$ |
1.488713160 |
\( -\frac{873722816}{59049} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 40 a^{3} - 121 a - 60\) , \( -152 a^{3} + 455 a + 218\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(40a^{3}-121a-60\right){x}-152a^{3}+455a+218$ |
| 9.1-a7 |
9.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$285.8329267$ |
1.488713160 |
\( -\frac{467951528}{3} a^{3} + \frac{2339757640}{3} a + 382083912 \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{3} - 4 a\) , \( -67 a^{3} + 35 a^{2} + 251 a - 129\) , \( 381 a^{3} - 197 a^{2} - 1422 a + 735\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-67a^{3}+35a^{2}+251a-129\right){x}+381a^{3}-197a^{2}-1422a+735$ |
| 9.1-a8 |
9.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$285.8329267$ |
1.488713160 |
\( \frac{320418987231990328}{27} a^{3} - \frac{1602094936159951640}{27} a + 29069000837710152 \) |
\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( a^{3} - 4 a\) , \( -372 a^{3} + 150 a^{2} + 1225 a - 878\) , \( 5455 a^{3} - 2171 a^{2} - 18929 a + 10866\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-372a^{3}+150a^{2}+1225a-878\right){x}+5455a^{3}-2171a^{2}-18929a+10866$ |
| 9.1-b1 |
9.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$3.210189511$ |
0.417993425 |
\( \frac{320418987231990328}{27} a^{3} - \frac{1602094936159951640}{27} a + 29069000837710152 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -370 a^{3} + 152 a^{2} + 1216 a - 885\) , \( -5826 a^{3} + 2322 a^{2} + 20149 a - 11749\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-370a^{3}+152a^{2}+1216a-885\right){x}-5826a^{3}+2322a^{2}+20149a-11749$ |
| 9.1-b2 |
9.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2006.368444$ |
0.417993425 |
\( -\frac{467951528}{3} a^{3} + \frac{2339757640}{3} a + 382083912 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 4 a + 1\) , \( a^{2} - 2\) , \( -71 a^{3} + 34 a^{2} + 265 a - 128\) , \( -251 a^{3} + 128 a^{2} + 937 a - 478\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+1\right){x}^{2}+\left(-71a^{3}+34a^{2}+265a-128\right){x}-251a^{3}+128a^{2}+937a-478$ |
| 9.1-b3 |
9.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{40} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$1.605094755$ |
0.417993425 |
\( -\frac{873722816}{59049} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a - 1\) , \( a^{3} - 3 a + 1\) , \( 39 a^{3} - 117 a - 60\) , \( 152 a^{3} - 456 a - 220\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(39a^{3}-117a-60\right){x}+152a^{3}-456a-220$ |
| 9.1-b4 |
9.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1003.184222$ |
0.417993425 |
\( \frac{64}{9} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 3 a + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}$ |
| 9.1-b5 |
9.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$6.420379023$ |
0.417993425 |
\( \frac{58591911104}{243} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a\) , \( a^{3} - 3 a + 1\) , \( -162 a^{3} + 486 a - 243\) , \( -1495 a^{3} + 4485 a - 2130\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(-162a^{3}+486a-243\right){x}-1495a^{3}+4485a-2130$ |
| 9.1-b6 |
9.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$4012.736889$ |
0.417993425 |
\( \frac{85184}{3} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a\) , \( a^{3} - 3 a + 1\) , \( -2 a^{3} + 6 a - 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(-2a^{3}+6a-3\right){x}$ |
| 9.1-b7 |
9.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2006.368444$ |
0.417993425 |
\( \frac{467951528}{3} a^{3} - \frac{2339757640}{3} a + 382083912 \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 1\) , \( -4 a^{3} + 9 a - 11\) , \( 6 a^{3} - 3 a^{2} - 25 a + 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-4a^{3}+9a-11\right){x}+6a^{3}-3a^{2}-25a+6$ |
| 9.1-b8 |
9.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$5.64495$ |
$(a^2-2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$3.210189511$ |
0.417993425 |
\( -\frac{320418987231990328}{27} a^{3} + \frac{1602094936159951640}{27} a + 29069000837710152 \) |
\( \bigl[a + 1\) , \( a^{3} - 5 a + 1\) , \( a^{3} - 3 a + 1\) , \( -2461 a^{3} + 1265 a^{2} + 9161 a - 4781\) , \( -87314 a^{3} + 45141 a^{2} + 325764 a - 168705\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-2461a^{3}+1265a^{2}+9161a-4781\right){x}-87314a^{3}+45141a^{2}+325764a-168705$ |
| 16.1-a1 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-24$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$796.3913345$ |
1.036967883 |
\( -1707264 a^{3} + 5121792 a + 2417472 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -5 a^{2} - 12 a - 5\) , \( -10 a^{3} - 16 a^{2} + 12 a + 9\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}-a{x}^{2}+\left(-5a^{2}-12a-5\right){x}-10a^{3}-16a^{2}+12a+9$ |
| 16.1-a2 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-24$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$796.3913345$ |
1.036967883 |
\( 1707264 a^{3} - 5121792 a + 2417472 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{2} - a + 2\) , \( 0\) , \( -5 a^{2} + 10 a - 2\) , \( -10 a^{3} + 11 a^{2} + 23 a - 13\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-5a^{2}+10a-2\right){x}-10a^{3}+11a^{2}+23a-13$ |
| 16.1-a3 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-24$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$796.3913345$ |
1.036967883 |
\( -1707264 a^{3} + 5121792 a + 2417472 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{2} - a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -10 a^{3} + 3 a^{2} + 38 a - 21\) , \( -27 a^{3} + 15 a^{2} + 97 a - 53\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-10a^{3}+3a^{2}+38a-21\right){x}-27a^{3}+15a^{2}+97a-53$ |
| 16.1-a4 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-24$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$796.3913345$ |
1.036967883 |
\( 1707264 a^{3} - 5121792 a + 2417472 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a\) , \( 0\) , \( 10 a^{3} + 5 a^{2} - 40 a - 22\) , \( -17 a^{3} - 11 a^{2} + 58 a + 31\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}-a{x}^{2}+\left(10a^{3}+5a^{2}-40a-22\right){x}-17a^{3}-11a^{2}+58a+31$ |
| 16.1-a5 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-96$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$199.0978336$ |
1.036967883 |
\( 6508137062232 a^{3} - 3368859648336 a^{2} - 24288698179512 a + 12572755370856 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -7 a^{3} + 5 a^{2} + 23 a - 17\) , \( 8 a^{3} - 4 a^{2} - 32 a + 14\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-7a^{3}+5a^{2}+23a-17\right){x}+8a^{3}-4a^{2}-32a+14$ |
| 16.1-a6 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-96$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$199.0978336$ |
1.036967883 |
\( -1743850069416 a^{3} + 3368859648336 a^{2} + 467263215432 a - 902683222488 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 4 a^{3} - 5 a^{2} - 10 a + 3\) , \( -a^{3} + 3 a^{2} - 5 a\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(4a^{3}-5a^{2}-10a+3\right){x}-a^{3}+3a^{2}-5a$ |
| 16.1-a7 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-96$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$199.0978336$ |
1.036967883 |
\( -6508137062232 a^{3} - 3368859648336 a^{2} + 24288698179512 a + 12572755370856 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a + 1\) , \( a^{2} - 1\) , \( 9 a^{3} + 5 a^{2} - 35 a - 16\) , \( 16 a^{3} + 8 a^{2} - 60 a - 31\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(9a^{3}+5a^{2}-35a-16\right){x}+16a^{3}+8a^{2}-60a-31$ |
| 16.1-a8 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-96$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$199.0978336$ |
1.036967883 |
\( 1743850069416 a^{3} + 3368859648336 a^{2} - 467263215432 a - 902683222488 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a + 1\) , \( a^{2} - 1\) , \( -2 a^{3} - 5 a^{2} - 2 a + 4\) , \( -4 a^{3} - 9 a^{2} + 3\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-2a^{3}-5a^{2}-2a+4\right){x}-4a^{3}-9a^{2}+3$ |
| 16.1-a9 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-96$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$199.0978336$ |
1.036967883 |
\( -6508137062232 a^{3} - 3368859648336 a^{2} + 24288698179512 a + 12572755370856 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 7 a^{3} + 5 a^{2} - 25 a - 17\) , \( -8 a^{3} - 4 a^{2} + 30 a + 14\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(7a^{3}+5a^{2}-25a-17\right){x}-8a^{3}-4a^{2}+30a+14$ |
| 16.1-a10 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-96$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$199.0978336$ |
1.036967883 |
\( 1743850069416 a^{3} + 3368859648336 a^{2} - 467263215432 a - 902683222488 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -4 a^{3} - 5 a^{2} + 8 a + 3\) , \( a^{3} + 3 a^{2} + 3 a\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-4a^{3}-5a^{2}+8a+3\right){x}+a^{3}+3a^{2}+3a$ |
| 16.1-a11 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-96$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$199.0978336$ |
1.036967883 |
\( 6508137062232 a^{3} - 3368859648336 a^{2} - 24288698179512 a + 12572755370856 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a + 1\) , \( a^{2} - 1\) , \( -9 a^{3} + 5 a^{2} + 33 a - 16\) , \( -16 a^{3} + 8 a^{2} + 60 a - 31\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-9a^{3}+5a^{2}+33a-16\right){x}-16a^{3}+8a^{2}+60a-31$ |
| 16.1-a12 |
16.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-96$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$199.0978336$ |
1.036967883 |
\( -1743850069416 a^{3} + 3368859648336 a^{2} + 467263215432 a - 902683222488 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a + 1\) , \( a^{2} - 1\) , \( 2 a^{3} - 5 a^{2} + 4\) , \( 4 a^{3} - 9 a^{2} + 3\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(2a^{3}-5a^{2}+4\right){x}+4a^{3}-9a^{2}+3$ |
| 16.1-b1 |
16.1-b |
$16$ |
$48$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-192$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$626.2283084$ |
0.815401443 |
\( -600840130180059000 a^{3} + 1160733998424384000 a^{2} + 160994627660022750 a - 311017737504159000 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 1\) , \( a^{3} - 4 a + 1\) , \( -49 a^{3} - 26 a^{2} + 177 a + 85\) , \( -168 a^{3} - 86 a^{2} + 634 a + 334\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(-49a^{3}-26a^{2}+177a+85\right){x}-168a^{3}-86a^{2}+634a+334$ |
| 16.1-b2 |
16.1-b |
$16$ |
$48$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$2504.913233$ |
0.815401443 |
\( 818626500 a^{2} - 219348000 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 1\) , \( a^{3} - 4 a + 1\) , \( 11 a^{3} + 4 a^{2} - 48 a - 25\) , \( -5 a^{3} + a^{2} + 25 a + 10\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(11a^{3}+4a^{2}-48a-25\right){x}-5a^{3}+a^{2}+25a+10$ |
| 16.1-b3 |
16.1-b |
$16$ |
$48$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-192$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$626.2283084$ |
0.815401443 |
\( 600840130180059000 a^{3} + 1160733998424384000 a^{2} - 160994627660022750 a - 311017737504159000 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 49 a^{3} - 27 a^{2} - 175 a + 89\) , \( 81 a^{3} - 38 a^{2} - 313 a + 160\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(49a^{3}-27a^{2}-175a+89\right){x}+81a^{3}-38a^{2}-313a+160$ |
| 16.1-b4 |
16.1-b |
$16$ |
$48$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$6.06589$ |
$(a^3-4a+1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-192$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$626.2283084$ |
0.815401443 |
\( 2242365893060213250 a^{3} - 1160733998424384000 a^{2} - 8368623442060794000 a + 4331918256193377000 \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{2} + 3\) , \( a + 1\) , \( 19 a^{3} + 25 a^{2} - 28 a - 17\) , \( 38 a^{3} + 86 a^{2} + 15 a - 10\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(19a^{3}+25a^{2}-28a-17\right){x}+38a^{3}+86a^{2}+15a-10$ |
*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.
