| 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 |
| 8.1-a1 |
8.1-a |
$4$ |
$21$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$1.13736$ |
$(2)$ |
0 |
$\Z/21\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$386.8008344$ |
0.292366465 |
\( -\frac{140625}{8} \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 2\) , \( 13 a^{2} + 2 a - 44\) , \( -22 a^{2} - 3 a + 88\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(13a^{2}+2a-44\right){x}-22a^{2}-3a+88$ |
| 8.1-a2 |
8.1-a |
$4$ |
$21$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{63} \) |
$1.13736$ |
$(2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.3 |
$1$ |
\( 3 \cdot 7 \) |
$1$ |
$1.127699225$ |
0.292366465 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[a\) , \( -1\) , \( a^{2} - 1\) , \( 125040 a^{2} - 43189 a - 360486\) , \( 56242078 a^{2} - 19527401 a - 161952511\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-1\right){y}={x}^{3}-{x}^{2}+\left(125040a^{2}-43189a-360486\right){x}+56242078a^{2}-19527401a-161952511$ |
| 8.1-a3 |
8.1-a |
$4$ |
$21$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$1.13736$ |
$(2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$128.9336114$ |
0.292366465 |
\( \frac{3375}{2} \) |
\( \bigl[1\) , \( a^{2} + a - 3\) , \( a^{2} + a - 1\) , \( -a^{2} + 4\) , \( -a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-a^{2}+4\right){x}-a-2$ |
| 8.1-a4 |
8.1-a |
$4$ |
$21$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{21} \) |
$1.13736$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.1.3 |
$1$ |
\( 7 \) |
$1$ |
$0.375899741$ |
0.292366465 |
\( -\frac{189613868625}{128} \) |
\( \bigl[a + 1\) , \( -a\) , \( a^{2} - 1\) , \( 17115 a^{2} - 5866 a - 49431\) , \( 1410206 a^{2} - 489214 a - 4061553\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}-a{x}^{2}+\left(17115a^{2}-5866a-49431\right){x}+1410206a^{2}-489214a-4061553$ |
| 17.1-a1 |
17.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$1.28960$ |
$(2a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$18.26148809$ |
0.507263558 |
\( -\frac{7715927403056521557}{17} a^{2} + \frac{2679713465103470916}{17} a + \frac{22217127489402511122}{17} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( 0\) , \( 99 a^{2} - 64 a - 331\) , \( 958 a^{2} - 218 a - 2583\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(99a^{2}-64a-331\right){x}+958a^{2}-218a-2583$ |
| 17.1-a2 |
17.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{4} \) |
$1.28960$ |
$(2a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.565372023$ |
0.507263558 |
\( \frac{261445487080230981}{83521} a^{2} - \frac{400557711948933636}{83521} a - \frac{170646420428250786}{83521} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( 0\) , \( -11 a^{2} - 24 a - 21\) , \( -38 a^{2} - 104 a - 85\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-11a^{2}-24a-21\right){x}-38a^{2}-104a-85$ |
| 17.1-a3 |
17.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$1.28960$ |
$(2a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$36.52297618$ |
0.507263558 |
\( -\frac{119617489449}{289} a^{2} + \frac{41241472785}{289} a + \frac{344991489660}{289} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( 0\) , \( 4 a^{2} - 4 a - 16\) , \( 20 a^{2} - 7 a - 58\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(4a^{2}-4a-16\right){x}+20a^{2}-7a-58$ |
| 17.1-a4 |
17.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$1.28960$ |
$(2a^2-a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$73.04595237$ |
0.507263558 |
\( -\frac{219348}{17} a^{2} + \frac{90963}{17} a + \frac{633150}{17} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( 0\) , \( -a^{2} + a + 4\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{2}+a+4\right){x}$ |
| 17.1-a5 |
17.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$1.28960$ |
$(2a^2-a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$54.78446428$ |
0.507263558 |
\( \frac{11224223245743811083}{4913} a^{2} + \frac{21094639493182324371}{4913} a + \frac{5972284442955277116}{4913} \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( 1029 a^{2} - 331 a - 3016\) , \( 20866 a^{2} - 7345 a - 59899\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(1029a^{2}-331a-3016\right){x}+20866a^{2}-7345a-59899$ |
| 17.1-a6 |
17.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$1.28960$ |
$(2a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$109.5689285$ |
0.507263558 |
\( \frac{418603459872780}{24137569} a^{2} + \frac{786688502074839}{24137569} a + \frac{222772245824754}{24137569} \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( 79 a^{2} - 26 a - 231\) , \( 122 a^{2} - 44 a - 351\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(79a^{2}-26a-231\right){x}+122a^{2}-44a-351$ |
| 17.1-a7 |
17.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$1.28960$ |
$(2a^2-a-3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$219.1378571$ |
0.507263558 |
\( -\frac{170514783}{4913} a^{2} + \frac{42561684}{4913} a + \frac{469465740}{4913} \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( 44 a^{2} - 16 a - 126\) , \( -207 a^{2} + 71 a + 595\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(44a^{2}-16a-126\right){x}-207a^{2}+71a+595$ |
| 17.1-a8 |
17.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{12} \) |
$1.28960$ |
$(2a^2-a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$13.69611607$ |
0.507263558 |
\( \frac{4075073731548124101}{582622237229761} a^{2} - \frac{3433122709460467011}{582622237229761} a - \frac{810676269288190764}{582622237229761} \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( -311 a^{2} + 119 a + 874\) , \( 1414 a^{2} - 463 a - 4127\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-311a^{2}+119a+874\right){x}+1414a^{2}-463a-4127$ |
| 17.2-a1 |
17.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.2 |
\( 17 \) |
\( 17^{3} \) |
$1.28960$ |
$(a^2+a-3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$219.1378571$ |
0.507263558 |
\( \frac{42561684}{4913} a^{2} + \frac{127953099}{4913} a + \frac{43312806}{4913} \) |
\( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -30 a^{2} + 43 a + 21\) , \( 103 a^{2} - 160 a - 66\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-30a^{2}+43a+21\right){x}+103a^{2}-160a-66$ |
| 17.2-a2 |
17.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{12} \) |
$1.28960$ |
$(a^2+a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$13.69611607$ |
0.507263558 |
\( -\frac{3433122709460467011}{582622237229761} a^{2} - \frac{641951022087657090}{582622237229761} a + \frac{14205716612728991460}{582622237229761} \) |
\( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -455 a^{2} + 738 a + 216\) , \( 7473 a^{2} - 11274 a - 5210\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-455a^{2}+738a+216\right){x}+7473a^{2}-11274a-5210$ |
| 17.2-a3 |
17.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.2 |
\( 17 \) |
\( 17^{6} \) |
$1.28960$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$109.5689285$ |
0.507263558 |
\( \frac{786688502074839}{24137569} a^{2} - \frac{1205291961947619}{24137569} a - \frac{513397838579364}{24137569} \) |
\( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -475 a^{2} + 733 a + 296\) , \( 7691 a^{2} - 11788 a - 5014\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-475a^{2}+733a+296\right){x}+7691a^{2}-11788a-5014$ |
| 17.2-a4 |
17.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.2 |
\( 17 \) |
\( 17^{3} \) |
$1.28960$ |
$(a^2+a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$54.78446428$ |
0.507263558 |
\( \frac{21094639493182324371}{4913} a^{2} - \frac{32318862738926135454}{4913} a - \frac{13768548051921749460}{4913} \) |
\( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -7615 a^{2} + 11768 a + 4776\) , \( 514961 a^{2} - 789514 a - 335090\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7615a^{2}+11768a+4776\right){x}+514961a^{2}-789514a-335090$ |
| 17.2-a5 |
17.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$1.28960$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$18.26148809$ |
0.507263558 |
\( \frac{2679713465103470916}{17} a^{2} + \frac{5036213937953050641}{17} a + \frac{1425845753082526176}{17} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -64 a^{2} - 35 a - 5\) , \( -218 a^{2} - 740 a - 231\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-64a^{2}-35a-5\right){x}-218a^{2}-740a-231$ |
| 17.2-a6 |
17.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.2 |
\( 17 \) |
\( 17^{2} \) |
$1.28960$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$36.52297618$ |
0.507263558 |
\( \frac{41241472785}{289} a^{2} + \frac{78376016664}{289} a + \frac{23273565192}{289} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -4 a^{2}\) , \( -7 a^{2} - 13 a - 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}-4a^{2}{x}-7a^{2}-13a-4$ |
| 17.2-a7 |
17.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$1.28960$ |
$(a^2+a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$73.04595237$ |
0.507263558 |
\( \frac{90963}{17} a^{2} + \frac{128385}{17} a + \frac{12528}{17} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( a^{2}\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+a^{2}{x}$ |
| 17.2-a8 |
17.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{4} \) |
$1.28960$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.565372023$ |
0.507263558 |
\( -\frac{400557711948933636}{83521} a^{2} + \frac{139112224868702655}{83521} a + \frac{1153359977630078448}{83521} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -24 a^{2} + 35 a + 5\) , \( -104 a^{2} + 142 a + 47\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-24a^{2}+35a+5\right){x}-104a^{2}+142a+47$ |
| 17.3-a1 |
17.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.3 |
\( 17 \) |
\( 17^{3} \) |
$1.28960$ |
$(a^2-2a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$54.78446428$ |
0.507263558 |
\( -\frac{32318862738926135454}{4913} a^{2} + \frac{11224223245743811083}{4913} a + \frac{93058456412295170190}{4913} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 1\) , \( a\) , \( 28433 a^{2} - 9539 a - 82497\) , \( -3025589 a^{2} + 1055150 a + 8703613\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(28433a^{2}-9539a-82497\right){x}-3025589a^{2}+1055150a+8703613$ |
| 17.3-a2 |
17.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.3 |
\( 17 \) |
\( - 17^{12} \) |
$1.28960$ |
$(a^2-2a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$13.69611607$ |
0.507263558 |
\( -\frac{641951022087657090}{582622237229761} a^{2} + \frac{4075073731548124101}{582622237229761} a + \frac{8623373237983371618}{582622237229761} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 1\) , \( a\) , \( 1913 a^{2} - 759 a - 5327\) , \( -44365 a^{2} + 15660 a + 127267\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(1913a^{2}-759a-5327\right){x}-44365a^{2}+15660a+127267$ |
| 17.3-a3 |
17.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.3 |
\( 17 \) |
\( 17^{6} \) |
$1.28960$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$109.5689285$ |
0.507263558 |
\( -\frac{1205291961947619}{24137569} a^{2} + \frac{418603459872780}{24137569} a + \frac{3470563089465552}{24137569} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 1\) , \( a\) , \( 1773 a^{2} - 589 a - 5152\) , \( -46301 a^{2} + 16115 a + 133250\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(1773a^{2}-589a-5152\right){x}-46301a^{2}+16115a+133250$ |
| 17.3-a4 |
17.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.3 |
\( 17 \) |
\( 17^{3} \) |
$1.28960$ |
$(a^2-2a-3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$219.1378571$ |
0.507263558 |
\( \frac{127953099}{4913} a^{2} - \frac{170514783}{4913} a - \frac{127470024}{4913} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 1\) , \( a\) , \( 98 a^{2} - 19 a - 307\) , \( -668 a^{2} + 195 a + 1990\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(98a^{2}-19a-307\right){x}-668a^{2}+195a+1990$ |
| 17.3-a5 |
17.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.3 |
\( 17 \) |
\( - 17^{4} \) |
$1.28960$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.565372023$ |
0.507263558 |
\( \frac{139112224868702655}{83521} a^{2} + \frac{261445487080230981}{83521} a + \frac{74020103994805866}{83521} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( a^{2} + a - 1\) , \( 35 a^{2} - 8 a - 113\) , \( 133 a^{2} - 47 a - 411\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(35a^{2}-8a-113\right){x}+133a^{2}-47a-411$ |
| 17.3-a6 |
17.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.3 |
\( 17 \) |
\( 17 \) |
$1.28960$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$18.26148809$ |
0.507263558 |
\( \frac{5036213937953050641}{17} a^{2} - \frac{7715927403056521557}{17} a - \frac{3287155192616633274}{17} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( a^{2} + a - 1\) , \( -35 a^{2} + 102 a - 63\) , \( -639 a^{2} + 789 a + 777\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-35a^{2}+102a-63\right){x}-639a^{2}+789a+777$ |
| 17.3-a7 |
17.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.3 |
\( 17 \) |
\( 17^{2} \) |
$1.28960$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$36.52297618$ |
0.507263558 |
\( \frac{78376016664}{289} a^{2} - \frac{119617489449}{289} a - \frac{50995522566}{289} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( a^{2} + a - 1\) , \( 7 a - 8\) , \( -7 a^{2} + 11 a + 7\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(7a-8\right){x}-7a^{2}+11a+7$ |
| 17.3-a8 |
17.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
17.3 |
\( 17 \) |
\( 17 \) |
$1.28960$ |
$(a^2-2a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$73.04595237$ |
0.507263558 |
\( \frac{128385}{17} a^{2} - \frac{219348}{17} a - \frac{62316}{17} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( a^{2} + a - 1\) , \( 2 a + 2\) , \( a^{2} + a - 1\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(2a+2\right){x}+a^{2}+a-1$ |
| 27.1-a1 |
27.1-a |
$4$ |
$27$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$1.39297$ |
$(-a^2+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.837900525$ |
0.612633508 |
\( -12288000 \) |
\( \bigl[0\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( 280 a^{2} - 89 a - 818\) , \( 2805 a^{2} - 963 a - 8098\bigr] \) |
${y}^2+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(280a^{2}-89a-818\right){x}+2805a^{2}-963a-8098$ |
| 27.1-a2 |
27.1-a |
$4$ |
$27$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$1.39297$ |
$(-a^2+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$49.62331419$ |
0.612633508 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( a + 2\) , \( 12 a^{2} - 4 a - 35\bigr] \) |
${y}^2+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a+2\right){x}+12a^{2}-4a-35$ |
| 27.1-a3 |
27.1-a |
$4$ |
$27$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$1.39297$ |
$(-a^2+1)$ |
0 |
$\Z/9\Z$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$446.6098277$ |
0.612633508 |
\( -12288000 \) |
\( \bigl[0\) , \( a^{2} - 1\) , \( a + 1\) , \( 17 a^{2} - 3 a - 53\) , \( -56 a^{2} + 17 a + 164\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(17a^{2}-3a-53\right){x}-56a^{2}+17a+164$ |
| 27.1-a4 |
27.1-a |
$4$ |
$27$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$1.39297$ |
$(-a^2+1)$ |
0 |
$\Z/9\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$148.8699425$ |
0.612633508 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}$ |
| 51.1-a1 |
51.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( - 3^{8} \cdot 17^{8} \) |
$1.54873$ |
$(-a^2+1), (a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.476452004$ |
0.656200891 |
\( -\frac{73067274470120883503414977}{188345450907} a^{2} + \frac{25375998117751504521013489}{188345450907} a + \frac{70129610583765315423118325}{62781816969} \) |
\( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( 417 a^{2} - 133 a - 1203\) , \( 4217 a^{2} - 237 a - 14449\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(417a^{2}-133a-1203\right){x}+4217a^{2}-237a-14449$ |
| 51.1-a2 |
51.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( - 3^{4} \cdot 17 \) |
$1.54873$ |
$(-a^2+1), (a^2-2a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$47.24646415$ |
0.656200891 |
\( \frac{9123267589576143071594}{153} a^{2} + \frac{17146134462759887246327}{153} a + \frac{4854389290588414014785}{153} \) |
\( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( 27 a^{2} - 58 a - 43\) , \( 50 a^{2} - 62 a + 9\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(27a^{2}-58a-43\right){x}+50a^{2}-62a+9$ |
| 51.1-a3 |
51.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{16} \cdot 17^{4} \) |
$1.54873$ |
$(-a^2+1), (a^2-2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.81161603$ |
0.656200891 |
\( -\frac{736214157382250}{60886809} a^{2} + \frac{257154008212105}{60886809} a + \frac{2126010334493071}{60886809} \) |
\( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( -33 a^{2} + 92 a - 33\) , \( -292 a^{2} + 546 a + 23\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-33a^{2}+92a-33\right){x}-292a^{2}+546a+23$ |
| 51.1-a4 |
51.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{8} \cdot 17^{2} \) |
$1.54873$ |
$(-a^2+1), (a^2-2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$94.49292831$ |
0.656200891 |
\( \frac{21862041663547}{7803} a^{2} + \frac{41087226515522}{7803} a + \frac{3877536454165}{2601} \) |
\( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( -3 a^{2} + 17 a + 2\) , \( 11 a^{2} - 8 a - 6\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-3a^{2}+17a+2\right){x}+11a^{2}-8a-6$ |
| 51.1-a5 |
51.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{4} \cdot 17 \) |
$1.54873$ |
$(-a^2+1), (a^2-2a-3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$188.9858566$ |
0.656200891 |
\( \frac{57227017}{153} a^{2} - \frac{97672967}{153} a - \frac{40772771}{153} \) |
\( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( -3 a^{2} + 17 a + 7\) , \( 17 a^{2} - 13 a - 7\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-3a^{2}+17a+7\right){x}+17a^{2}-13a-7$ |
| 51.1-a6 |
51.1-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{32} \cdot 17^{2} \) |
$1.54873$ |
$(-a^2+1), (a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.476452004$ |
0.656200891 |
\( \frac{51150856611467521}{51195483} a^{2} - \frac{78367545688483633}{51195483} a - \frac{3709618270320887}{5688387} \) |
\( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( -963 a^{2} + 1517 a + 577\) , \( -24013 a^{2} + 36905 a + 15491\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-963a^{2}+1517a+577\right){x}-24013a^{2}+36905a+15491$ |
| 51.2-a1 |
51.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.2 |
\( 3 \cdot 17 \) |
\( 3^{32} \cdot 17^{2} \) |
$1.54873$ |
$(-a^2+1), (2a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.476452004$ |
0.656200891 |
\( -\frac{78367545688483633}{51195483} a^{2} + \frac{9072229692338704}{17065161} a + \frac{225650240167014325}{51195483} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( 1510 a^{2} - 544 a - 4379\) , \( 37713 a^{2} - 13154 a - 108667\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(1510a^{2}-544a-4379\right){x}+37713a^{2}-13154a-108667$ |
| 51.2-a2 |
51.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.2 |
\( 3 \cdot 17 \) |
\( 3^{16} \cdot 17^{4} \) |
$1.54873$ |
$(-a^2+1), (2a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.81161603$ |
0.656200891 |
\( \frac{257154008212105}{60886809} a^{2} + \frac{479060149170145}{60886809} a + \frac{139274003304361}{60886809} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( 85 a^{2} - 49 a - 279\) , \( 599 a^{2} - 256 a - 1795\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(85a^{2}-49a-279\right){x}+599a^{2}-256a-1795$ |
| 51.2-a3 |
51.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.2 |
\( 3 \cdot 17 \) |
\( - 3^{8} \cdot 17^{8} \) |
$1.54873$ |
$(-a^2+1), (2a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.476452004$ |
0.656200891 |
\( \frac{25375998117751504521013489}{188345450907} a^{2} + \frac{15897092117456459660800496}{62781816969} a + \frac{13502286575551170220498043}{188345450907} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( -140 a^{2} - 274 a - 99\) , \( -139 a^{2} - 3802 a - 5503\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-140a^{2}-274a-99\right){x}-139a^{2}-3802a-5503$ |
| 51.2-a4 |
51.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.2 |
\( 3 \cdot 17 \) |
\( 3^{8} \cdot 17^{2} \) |
$1.54873$ |
$(-a^2+1), (2a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$94.49292831$ |
0.656200891 |
\( \frac{41087226515522}{7803} a^{2} - \frac{20983089393023}{2601} a - \frac{26817760341455}{7803} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( 10 a^{2} - 4 a - 34\) , \( -5 a^{2} + 15\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(10a^{2}-4a-34\right){x}-5a^{2}+15$ |
| 51.2-a5 |
51.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.2 |
\( 3 \cdot 17 \) |
\( 3^{4} \cdot 17 \) |
$1.54873$ |
$(-a^2+1), (2a^2-a-3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$188.9858566$ |
0.656200891 |
\( -\frac{97672967}{153} a^{2} + \frac{40445950}{153} a + \frac{269027197}{153} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( 10 a^{2} - 4 a - 29\) , \( -15 a^{2} + 4 a + 41\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(10a^{2}-4a-29\right){x}-15a^{2}+4a+41$ |
| 51.2-a6 |
51.2-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.2 |
\( 3 \cdot 17 \) |
\( - 3^{4} \cdot 17 \) |
$1.54873$ |
$(-a^2+1), (2a^2-a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$47.24646415$ |
0.656200891 |
\( \frac{17146134462759887246327}{153} a^{2} - \frac{26269402052336030317921}{153} a - \frac{11191344455779074334681}{153} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( -65 a^{2} + 41 a + 131\) , \( -29 a^{2} - 60 a + 261\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-65a^{2}+41a+131\right){x}-29a^{2}-60a+261$ |
| 51.3-a1 |
51.3-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.3 |
\( 3 \cdot 17 \) |
\( 3^{32} \cdot 17^{2} \) |
$1.54873$ |
$(-a^2+1), (a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.476452004$ |
0.656200891 |
\( \frac{9072229692338704}{17065161} a^{2} + \frac{51150856611467521}{51195483} a + \frac{14481770636014835}{51195483} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -543 a^{2} - 968 a - 272\) , \( -13153 a^{2} - 24560 a - 6934\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-543a^{2}-968a-272\right){x}-13153a^{2}-24560a-6934$ |
| 51.3-a2 |
51.3-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.3 |
\( 3 \cdot 17 \) |
\( - 3^{4} \cdot 17 \) |
$1.54873$ |
$(-a^2+1), (a^2+a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$47.24646415$ |
0.656200891 |
\( -\frac{26269402052336030317921}{153} a^{2} + \frac{9123267589576143071594}{153} a + \frac{75639728574412760793815}{153} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( 42 a^{2} + 22 a - 82\) , \( -59 a^{2} + 88 a + 322\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(42a^{2}+22a-82\right){x}-59a^{2}+88a+322$ |
| 51.3-a3 |
51.3-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.3 |
\( 3 \cdot 17 \) |
\( 3^{16} \cdot 17^{4} \) |
$1.54873$ |
$(-a^2+1), (a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.81161603$ |
0.656200891 |
\( \frac{479060149170145}{60886809} a^{2} - \frac{736214157382250}{60886809} a - \frac{304538278611719}{60886809} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -48 a^{2} - 38 a - 12\) , \( -255 a^{2} - 344 a - 86\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-48a^{2}-38a-12\right){x}-255a^{2}-344a-86$ |
| 51.3-a4 |
51.3-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.3 |
\( 3 \cdot 17 \) |
\( 3^{8} \cdot 17^{2} \) |
$1.54873$ |
$(-a^2+1), (a^2+a-3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$94.49292831$ |
0.656200891 |
\( -\frac{20983089393023}{2601} a^{2} + \frac{21862041663547}{7803} a + \frac{181255229047727}{7803} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -3 a^{2} - 8 a - 7\) , \( a^{2} + 4 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-3a^{2}-8a-7\right){x}+a^{2}+4a+4$ |
| 51.3-a5 |
51.3-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.3 |
\( 3 \cdot 17 \) |
\( 3^{4} \cdot 17 \) |
$1.54873$ |
$(-a^2+1), (a^2+a-3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$188.9858566$ |
0.656200891 |
\( \frac{40445950}{153} a^{2} + \frac{57227017}{153} a - \frac{7210637}{153} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -3 a^{2} - 8 a - 2\) , \( 5 a^{2} + 10 a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-3a^{2}-8a-2\right){x}+5a^{2}+10a+2$ |
| 51.3-a6 |
51.3-a |
$6$ |
$8$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
51.3 |
\( 3 \cdot 17 \) |
\( - 3^{8} \cdot 17^{8} \) |
$1.54873$ |
$(-a^2+1), (a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.476452004$ |
0.656200891 |
\( \frac{15897092117456459660800496}{62781816969} a^{2} - \frac{73067274470120883503414977}{188345450907} a - \frac{31128269893684578702277955}{188345450907} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -273 a^{2} + 412 a + 168\) , \( -3801 a^{2} + 3940 a + 1822\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-273a^{2}+412a+168\right){x}-3801a^{2}+3940a+1822$ |
*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.
