| 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 |
| 2.1-a1 |
2.1-a |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$27.35630$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$3.282840292$ |
1.47110584 |
\( \frac{35107015734019341864705051}{4} a^{4} - \frac{67461499648100497870746611}{4} a^{3} - \frac{81008349136479950786830423}{4} a^{2} + \frac{155665316532958596784779243}{4} a - \frac{18269717693460806606443579}{4} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a + 1\) , \( 531 a^{4} + 712 a^{3} - 2298 a^{2} - 3028 a + 402\) , \( 15151 a^{4} + 19696 a^{3} - 65672 a^{2} - 85123 a + 11735\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+4a+1\right){x}^{2}+\left(531a^{4}+712a^{3}-2298a^{2}-3028a+402\right){x}+15151a^{4}+19696a^{3}-65672a^{2}-85123a+11735$ |
| 2.1-a2 |
2.1-a |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$27.35630$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$105.0508893$ |
1.47110584 |
\( \frac{14648168417491}{16} a^{4} - \frac{28357895908847}{16} a^{3} - \frac{33072399519703}{16} a^{2} + \frac{64307418095571}{16} a - \frac{7552788056951}{16} \) |
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( -a^{3} + 4 a\) , \( a^{4} - 3 a^{2} + 1\) , \( -3 a^{4} + 13 a^{3} + 2 a^{2} - 48 a - 12\) , \( 6 a^{4} + 58 a^{3} - 52 a^{2} - 202 a - 7\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{4}-3a^{2}+1\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-3a^{4}+13a^{3}+2a^{2}-48a-12\right){x}+6a^{4}+58a^{3}-52a^{2}-202a-7$ |
| 2.1-a3 |
2.1-a |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{4} \) |
$27.35630$ |
$(-a^3+3a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6723.256919$ |
1.47110584 |
\( -\frac{17891}{16} a^{4} - \frac{9585}{16} a^{3} + \frac{60983}{16} a^{2} + \frac{43837}{16} a + \frac{17303}{16} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 1\) , \( a + 1\) , \( -a^{3} + a + 1\) , \( -a\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+1\right){x}^{2}+\left(-a^{3}+a+1\right){x}-a$ |
| 2.1-a4 |
2.1-a |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{8} \) |
$27.35630$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3361.628459$ |
1.47110584 |
\( \frac{169355571}{256} a^{4} + \frac{98155761}{256} a^{3} - \frac{308638359}{256} a^{2} - \frac{146361917}{256} a + \frac{23727033}{256} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a + 1\) , \( 41 a^{4} + 57 a^{3} - 163 a^{2} - 218 a + 32\) , \( 244 a^{4} + 326 a^{3} - 1019 a^{2} - 1334 a + 184\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+4a+1\right){x}^{2}+\left(41a^{4}+57a^{3}-163a^{2}-218a+32\right){x}+244a^{4}+326a^{3}-1019a^{2}-1334a+184$ |
| 2.1-a5 |
2.1-a |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{16} \) |
$27.35630$ |
$(-a^3+3a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1680.814229$ |
1.47110584 |
\( \frac{248146784615263411}{65536} a^{4} + \frac{509720083489414001}{65536} a^{3} - \frac{441861038816354583}{65536} a^{2} - \frac{907629911330953405}{65536} a + \frac{120805185588869433}{65536} \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{4} - 3 a^{2} + a + 1\) , \( -14 a^{4} - 21 a^{3} + 59 a^{2} + 87 a - 11\) , \( 193 a^{4} + 241 a^{3} - 836 a^{2} - 1051 a + 145\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{4}-3a^{2}+a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-14a^{4}-21a^{3}+59a^{2}+87a-11\right){x}+193a^{4}+241a^{3}-836a^{2}-1051a+145$ |
| 2.1-a6 |
2.1-a |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$27.35630$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$3.282840292$ |
1.47110584 |
\( -\frac{31757328991159534951451}{4} a^{4} + \frac{49240573667147018974195}{4} a^{3} + \frac{114195142809778251374679}{4} a^{2} - \frac{177062564753366183096299}{4} a + \frac{20481636247418622831483}{4} \) |
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( -a^{3} + 4 a\) , \( a^{4} - 3 a^{2} + 1\) , \( 107 a^{4} + 158 a^{3} - 453 a^{2} - 633 a + 73\) , \( 1358 a^{4} + 1845 a^{3} - 5773 a^{2} - 7670 a + 1013\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{4}-3a^{2}+1\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(107a^{4}+158a^{3}-453a^{2}-633a+73\right){x}+1358a^{4}+1845a^{3}-5773a^{2}-7670a+1013$ |
| 2.1-b1 |
2.1-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$27.35630$ |
$(-a^3+3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.071186912$ |
$1666.754773$ |
1.03847505 |
\( \frac{35107015734019341864705051}{4} a^{4} - \frac{67461499648100497870746611}{4} a^{3} - \frac{81008349136479950786830423}{4} a^{2} + \frac{155665316532958596784779243}{4} a - \frac{18269717693460806606443579}{4} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a\) , \( -557 a^{4} - 18 a^{3} + 3362 a^{2} + 221 a - 4585\) , \( 14586 a^{4} + 1565 a^{3} - 87558 a^{2} - 9950 a + 116599\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+4a\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-557a^{4}-18a^{3}+3362a^{2}+221a-4585\right){x}+14586a^{4}+1565a^{3}-87558a^{2}-9950a+116599$ |
| 2.1-b2 |
2.1-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$27.35630$ |
$(-a^3+3a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.035593456$ |
$13334.03818$ |
1.03847505 |
\( \frac{14648168417491}{16} a^{4} - \frac{28357895908847}{16} a^{3} - \frac{33072399519703}{16} a^{2} + \frac{64307418095571}{16} a - \frac{7552788056951}{16} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a\) , \( -2 a^{4} + 42 a^{3} + 67 a^{2} - 174 a - 260\) , \( 27 a^{4} - 219 a^{3} - 474 a^{2} + 901 a + 1561\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+4a\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-2a^{4}+42a^{3}+67a^{2}-174a-260\right){x}+27a^{4}-219a^{3}-474a^{2}+901a+1561$ |
| 2.1-b3 |
2.1-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{4} \) |
$27.35630$ |
$(-a^3+3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.008898364$ |
$13334.03818$ |
1.03847505 |
\( -\frac{17891}{16} a^{4} - \frac{9585}{16} a^{3} + \frac{60983}{16} a^{2} + \frac{43837}{16} a + \frac{17303}{16} \) |
\( \bigl[a\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a - 3\) , \( a^{4} - 3 a^{2}\) , \( -2 a^{2} - a + 7\) , \( -a^{4} + 4 a^{2} - a - 4\bigr] \) |
${y}^2+a{x}{y}+\left(a^{4}-3a^{2}\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a-3\right){x}^{2}+\left(-2a^{2}-a+7\right){x}-a^{4}+4a^{2}-a-4$ |
| 2.1-b4 |
2.1-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{8} \) |
$27.35630$ |
$(-a^3+3a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.017796728$ |
$26668.07637$ |
1.03847505 |
\( \frac{169355571}{256} a^{4} + \frac{98155761}{256} a^{3} - \frac{308638359}{256} a^{2} - \frac{146361917}{256} a + \frac{23727033}{256} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a\) , \( -2 a^{4} + 2 a^{3} + 12 a^{2} - 9 a - 20\) , \( -2 a^{3} - a^{2} + 7 a + 2\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+4a\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-2a^{4}+2a^{3}+12a^{2}-9a-20\right){x}-2a^{3}-a^{2}+7a+2$ |
| 2.1-b5 |
2.1-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{16} \) |
$27.35630$ |
$(-a^3+3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.035593456$ |
$3333.509546$ |
1.03847505 |
\( \frac{248146784615263411}{65536} a^{4} + \frac{509720083489414001}{65536} a^{3} - \frac{441861038816354583}{65536} a^{2} - \frac{907629911330953405}{65536} a + \frac{120805185588869433}{65536} \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -4 a^{4} - a^{3} + 14 a^{2} + a - 4\) , \( -3 a^{4} - a^{3} + 15 a^{2} + 10 a - 3\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a-1\right){x}^{2}+\left(-4a^{4}-a^{3}+14a^{2}+a-4\right){x}-3a^{4}-a^{3}+15a^{2}+10a-3$ |
| 2.1-b6 |
2.1-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$27.35630$ |
$(-a^3+3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.071186912$ |
$1666.754773$ |
1.03847505 |
\( -\frac{31757328991159534951451}{4} a^{4} + \frac{49240573667147018974195}{4} a^{3} + \frac{114195142809778251374679}{4} a^{2} - \frac{177062564753366183096299}{4} a + \frac{20481636247418622831483}{4} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a\) , \( 553 a^{4} + 742 a^{3} - 2348 a^{2} - 3209 a + 225\) , \( -14184 a^{4} - 18691 a^{3} + 60898 a^{2} + 80908 a - 8621\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+4a\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(553a^{4}+742a^{3}-2348a^{2}-3209a+225\right){x}-14184a^{4}-18691a^{3}+60898a^{2}+80908a-8621$ |
| 4.1-a1 |
4.1-a |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$29.31976$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 7$ |
2B, 7Ns |
$1$ |
\( 1 \) |
$1$ |
$1399.394852$ |
1.22479802 |
\( 6908228743682104 a^{4} - 13274818433086547 a^{3} - 15940534212321925 a^{2} + 30631230136396826 a - 3595022728230192 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -21 a^{4} - 5 a^{3} + 133 a^{2} + 27 a - 194\) , \( -116 a^{4} - 9 a^{3} + 688 a^{2} + 67 a - 889\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-21a^{4}-5a^{3}+133a^{2}+27a-194\right){x}-116a^{4}-9a^{3}+688a^{2}+67a-889$ |
| 4.1-a2 |
4.1-a |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$29.31976$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 7$ |
2B, 7Ns |
$1$ |
\( 1 \) |
$1$ |
$1399.394852$ |
1.22479802 |
\( -3925017565 a^{4} - 4983392400 a^{3} + 16949294508 a^{2} + 21691981177 a - 3004697106 \) |
\( \bigl[a^{2} - 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a - 3\) , \( a^{2} + a - 2\) , \( 8 a^{4} + 9 a^{3} - 36 a^{2} - 41 a + 8\) , \( -28 a^{4} - 44 a^{3} + 122 a^{2} + 184 a - 27\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a-3\right){x}^{2}+\left(8a^{4}+9a^{3}-36a^{2}-41a+8\right){x}-28a^{4}-44a^{3}+122a^{2}+184a-27$ |
| 4.1-b1 |
4.1-b |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$29.31976$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 7$ |
2B, 7Ns |
$1$ |
\( 3 \) |
$1$ |
$403.8330233$ |
1.06034523 |
\( 6908228743682104 a^{4} - 13274818433086547 a^{3} - 15940534212321925 a^{2} + 30631230136396826 a - 3595022728230192 \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{4} - 5 a^{2} + 4\) , \( a^{2} - 1\) , \( -5 a^{4} + 18 a^{3} + 14 a^{2} - 37 a - 1\) , \( -30 a^{4} + 33 a^{3} + 65 a^{2} - 83 a + 11\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-5a^{2}+4\right){x}^{2}+\left(-5a^{4}+18a^{3}+14a^{2}-37a-1\right){x}-30a^{4}+33a^{3}+65a^{2}-83a+11$ |
| 4.1-b2 |
4.1-b |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$29.31976$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 7$ |
2B, 7Ns |
$1$ |
\( 3 \) |
$1$ |
$403.8330233$ |
1.06034523 |
\( -3925017565 a^{4} - 4983392400 a^{3} + 16949294508 a^{2} + 21691981177 a - 3004697106 \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{2} - 3\) , \( a^{4} - 3 a^{2}\) , \( -6 a^{4} + 40 a^{2} + 3 a - 57\) , \( 30 a^{4} + 5 a^{3} - 179 a^{2} - 26 a + 235\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{4}-3a^{2}\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-6a^{4}+40a^{2}+3a-57\right){x}+30a^{4}+5a^{3}-179a^{2}-26a+235$ |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$33.67956$ |
$(-a^4+a^3+5a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$736.9458266$ |
1.29000016 |
\( -\frac{6811011}{4} a^{4} - 231226 a^{3} + \frac{20324635}{2} a^{2} + 1355614 a - \frac{53379719}{4} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 2 a + 2\) , \( a^{4} - 3 a^{2} + 1\) , \( 17 a^{4} + 19 a^{3} - 72 a^{2} - 85 a + 13\) , \( -71 a^{4} - 92 a^{3} + 302 a^{2} + 390 a - 54\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{4}-3a^{2}+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+2\right){x}^{2}+\left(17a^{4}+19a^{3}-72a^{2}-85a+13\right){x}-71a^{4}-92a^{3}+302a^{2}+390a-54$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{4} \) |
$33.67956$ |
$(-a^4+a^3+5a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$368.4729133$ |
1.29000016 |
\( 21952437077625 a^{4} + 2777305092038 a^{3} - \frac{262726502375931}{2} a^{2} - 16619379508139 a + \frac{347033795558241}{2} \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{4} + 4 a^{2} - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a\) , \( a^{4} + 4 a^{3} - 6 a^{2} - 18 a + 1\) , \( 5 a^{4} + 5 a^{3} - 23 a^{2} - 25 a + 3\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+4a\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-1\right){x}^{2}+\left(a^{4}+4a^{3}-6a^{2}-18a+1\right){x}+5a^{4}+5a^{3}-23a^{2}-25a+3$ |
| 16.1-b1 |
16.1-b |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$33.67956$ |
$(-a^4+a^3+5a^2-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.028173912$ |
$6554.920734$ |
1.61636268 |
\( -\frac{6811011}{4} a^{4} - 231226 a^{3} + \frac{20324635}{2} a^{2} + 1355614 a - \frac{53379719}{4} \) |
\( \bigl[a\) , \( -a^{2} - a + 2\) , \( a^{4} - 3 a^{2} + a + 1\) , \( a^{4} - 5 a^{2} - 3 a + 1\) , \( -2 a^{4} - 5 a^{3} + a^{2} + 6 a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{4}-3a^{2}+a+1\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(a^{4}-5a^{2}-3a+1\right){x}-2a^{4}-5a^{3}+a^{2}+6a-1$ |
| 16.1-b2 |
16.1-b |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{4} \) |
$33.67956$ |
$(-a^4+a^3+5a^2-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.056347825$ |
$6554.920734$ |
1.61636268 |
\( 21952437077625 a^{4} + 2777305092038 a^{3} - \frac{262726502375931}{2} a^{2} - 16619379508139 a + \frac{347033795558241}{2} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 5 a + 4\) , \( 1\) , \( -3 a^{4} - 8 a^{3} - 3 a^{2} + 10 a + 13\) , \( -21 a^{4} - 46 a^{3} + 31 a^{2} + 81 a + 1\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+{y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+5a+4\right){x}^{2}+\left(-3a^{4}-8a^{3}-3a^{2}+10a+13\right){x}-21a^{4}-46a^{3}+31a^{2}+81a+1$ |
| 16.2-a1 |
16.2-a |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{4} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 7$ |
2B, 7Ns |
$1$ |
\( 1 \) |
$1$ |
$1564.724894$ |
1.36950050 |
\( 6908228743682104 a^{4} - 13274818433086547 a^{3} - 15940534212321925 a^{2} + 30631230136396826 a - 3595022728230192 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( a^{4} - 4 a^{2} + 2\) , \( a + 1\) , \( 24 a^{4} - 51 a^{3} - 96 a^{2} + 166 a - 18\) , \( -18 a^{4} + 65 a^{3} + 85 a^{2} - 191 a + 23\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}-4a^{2}+2\right){x}^{2}+\left(24a^{4}-51a^{3}-96a^{2}+166a-18\right){x}-18a^{4}+65a^{3}+85a^{2}-191a+23$ |
| 16.2-a2 |
16.2-a |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{8} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 7$ |
2B, 7Ns |
$1$ |
\( 1 \) |
$1$ |
$1564.724894$ |
1.36950050 |
\( -3925017565 a^{4} - 4983392400 a^{3} + 16949294508 a^{2} + 21691981177 a - 3004697106 \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( a^{3} - 2 a + 1\) , \( 4 a^{4} + 13 a^{3} - 11 a^{2} - 53 a - 27\) , \( -13 a^{4} - 36 a^{3} + 27 a^{2} + 154 a + 115\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){x}^{2}+\left(4a^{4}+13a^{3}-11a^{2}-53a-27\right){x}-13a^{4}-36a^{3}+27a^{2}+154a+115$ |
| 16.2-b1 |
16.2-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{14} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$108.4541973$ |
1.51876490 |
\( \frac{35107015734019341864705051}{4} a^{4} - \frac{67461499648100497870746611}{4} a^{3} - \frac{81008349136479950786830423}{4} a^{2} + \frac{155665316532958596784779243}{4} a - \frac{18269717693460806606443579}{4} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 2\) , \( a^{4} - 3 a^{2}\) , \( 115 a^{4} - 233 a^{3} - 361 a^{2} + 882 a - 363\) , \( 2526 a^{4} - 3563 a^{3} - 9519 a^{2} + 12578 a + 271\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{4}-3a^{2}\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(115a^{4}-233a^{3}-361a^{2}+882a-363\right){x}+2526a^{4}-3563a^{3}-9519a^{2}+12578a+271$ |
| 16.2-b2 |
16.2-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$433.8167893$ |
1.51876490 |
\( \frac{14648168417491}{16} a^{4} - \frac{28357895908847}{16} a^{3} - \frac{33072399519703}{16} a^{2} + \frac{64307418095571}{16} a - \frac{7552788056951}{16} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 2\) , \( a^{4} - 3 a^{2}\) , \( 165 a^{4} - 258 a^{3} - 591 a^{2} + 927 a - 123\) , \( 2235 a^{4} - 3459 a^{3} - 8049 a^{2} + 12432 a - 1406\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{4}-3a^{2}\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(165a^{4}-258a^{3}-591a^{2}+927a-123\right){x}+2235a^{4}-3459a^{3}-8049a^{2}+12432a-1406$ |
| 16.2-b3 |
16.2-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{16} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3470.534314$ |
1.51876490 |
\( -\frac{17891}{16} a^{4} - \frac{9585}{16} a^{3} + \frac{60983}{16} a^{2} + \frac{43837}{16} a + \frac{17303}{16} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 4 a + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a + 1\) , \( 2 a^{4} - 7 a^{2} + a + 2\) , \( -2 a^{4} - 5 a^{3} + 3 a^{2} + 11 a - 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+4a+1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){x}^{2}+\left(2a^{4}-7a^{2}+a+2\right){x}-2a^{4}-5a^{3}+3a^{2}+11a-3$ |
| 16.2-b4 |
16.2-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{20} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1735.267157$ |
1.51876490 |
\( \frac{169355571}{256} a^{4} + \frac{98155761}{256} a^{3} - \frac{308638359}{256} a^{2} - \frac{146361917}{256} a + \frac{23727033}{256} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 2\) , \( a^{4} - 3 a^{2}\) , \( 10 a^{4} - 18 a^{3} - 36 a^{2} + 62 a - 8\) , \( 40 a^{4} - 65 a^{3} - 146 a^{2} + 230 a - 26\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{4}-3a^{2}\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(10a^{4}-18a^{3}-36a^{2}+62a-8\right){x}+40a^{4}-65a^{3}-146a^{2}+230a-26$ |
| 16.2-b5 |
16.2-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{28} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$108.4541973$ |
1.51876490 |
\( \frac{248146784615263411}{65536} a^{4} + \frac{509720083489414001}{65536} a^{3} - \frac{441861038816354583}{65536} a^{2} - \frac{907629911330953405}{65536} a + \frac{120805185588869433}{65536} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -26 a^{4} + 50 a^{3} + 56 a^{2} - 108 a + 12\) , \( 115 a^{4} - 213 a^{3} - 297 a^{2} + 540 a - 64\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+3a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+a{x}^{2}+\left(-26a^{4}+50a^{3}+56a^{2}-108a+12\right){x}+115a^{4}-213a^{3}-297a^{2}+540a-64$ |
| 16.2-b6 |
16.2-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$13.55677466$ |
1.51876490 |
\( -\frac{31757328991159534951451}{4} a^{4} + \frac{49240573667147018974195}{4} a^{3} + \frac{114195142809778251374679}{4} a^{2} - \frac{177062564753366183096299}{4} a + \frac{20481636247418622831483}{4} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 1\) , \( a + 1\) , \( 53 a^{4} - 42 a^{3} - 103 a^{2} + 262 a - 226\) , \( 968 a^{4} - 1735 a^{3} - 4490 a^{2} + 5328 a + 1651\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-1\right){x}^{2}+\left(53a^{4}-42a^{3}-103a^{2}+262a-226\right){x}+968a^{4}-1735a^{3}-4490a^{2}+5328a+1651$ |
| 16.2-c1 |
16.2-c |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{14} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$31.10141509$ |
1.74214511 |
\( \frac{35107015734019341864705051}{4} a^{4} - \frac{67461499648100497870746611}{4} a^{3} - \frac{81008349136479950786830423}{4} a^{2} + \frac{155665316532958596784779243}{4} a - \frac{18269717693460806606443579}{4} \) |
\( \bigl[a + 1\) , \( a^{3} - 2 a + 1\) , \( a^{3} - 3 a\) , \( -168 a^{4} + 177 a^{3} + 289 a^{2} - 321 a + 20\) , \( -3165 a^{4} + 7300 a^{3} + 8160 a^{2} - 17473 a + 2035\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-2a+1\right){x}^{2}+\left(-168a^{4}+177a^{3}+289a^{2}-321a+20\right){x}-3165a^{4}+7300a^{3}+8160a^{2}-17473a+2035$ |
| 16.2-c2 |
16.2-c |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$497.6226415$ |
1.74214511 |
\( \frac{14648168417491}{16} a^{4} - \frac{28357895908847}{16} a^{3} - \frac{33072399519703}{16} a^{2} + \frac{64307418095571}{16} a - \frac{7552788056951}{16} \) |
\( \bigl[a^{4} - 4 a^{2} + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( a + 1\) , \( -505 a^{4} - 80 a^{3} + 3044 a^{2} + 445 a - 4074\) , \( -12291 a^{4} - 1518 a^{3} + 73490 a^{2} + 9165 a - 96952\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(-505a^{4}-80a^{3}+3044a^{2}+445a-4074\right){x}-12291a^{4}-1518a^{3}+73490a^{2}+9165a-96952$ |
| 16.2-c3 |
16.2-c |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{16} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$995.2452831$ |
1.74214511 |
\( -\frac{17891}{16} a^{4} - \frac{9585}{16} a^{3} + \frac{60983}{16} a^{2} + \frac{43837}{16} a + \frac{17303}{16} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{4} - 3 a^{2} + a\) , \( 0\) , \( 3 a^{4} + 6 a^{3} - 6 a^{2} - 11 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(a^{4}-3a^{2}+a\right){x}^{2}+\left(3a^{4}+6a^{3}-6a^{2}-11a+3\right){x}$ |
| 16.2-c4 |
16.2-c |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{20} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1990.490566$ |
1.74214511 |
\( \frac{169355571}{256} a^{4} + \frac{98155761}{256} a^{3} - \frac{308638359}{256} a^{2} - \frac{146361917}{256} a + \frac{23727033}{256} \) |
\( \bigl[a^{4} - 4 a^{2} + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( a + 1\) , \( -40 a^{4} - 5 a^{3} + 239 a^{2} + 30 a - 314\) , \( -84 a^{4} - 12 a^{3} + 499 a^{2} + 65 a - 658\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(-40a^{4}-5a^{3}+239a^{2}+30a-314\right){x}-84a^{4}-12a^{3}+499a^{2}+65a-658$ |
| 16.2-c5 |
16.2-c |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{28} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$497.6226415$ |
1.74214511 |
\( \frac{248146784615263411}{65536} a^{4} + \frac{509720083489414001}{65536} a^{3} - \frac{441861038816354583}{65536} a^{2} - \frac{907629911330953405}{65536} a + \frac{120805185588869433}{65536} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 7 a\) , \( a^{4} - 4 a^{2} + a + 2\) , \( -50 a^{4} + 45 a^{3} + 225 a^{2} - 89 a - 216\) , \( 119 a^{4} + 138 a^{3} - 893 a^{2} - 393 a + 1368\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{4}-4a^{2}+a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-7a\right){x}^{2}+\left(-50a^{4}+45a^{3}+225a^{2}-89a-216\right){x}+119a^{4}+138a^{3}-893a^{2}-393a+1368$ |
| 16.2-c6 |
16.2-c |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$62.20283019$ |
1.74214511 |
\( -\frac{31757328991159534951451}{4} a^{4} + \frac{49240573667147018974195}{4} a^{3} + \frac{114195142809778251374679}{4} a^{2} - \frac{177062564753366183096299}{4} a + \frac{20481636247418622831483}{4} \) |
\( \bigl[a^{4} - 4 a^{2} + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( a + 1\) , \( -215 a^{4} - 325 a^{3} + 1724 a^{2} + 1295 a - 3259\) , \( -20246 a^{4} + 998 a^{3} + 116082 a^{2} + 1893 a - 141881\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(-215a^{4}-325a^{3}+1724a^{2}+1295a-3259\right){x}-20246a^{4}+998a^{3}+116082a^{2}+1893a-141881$ |
| 16.2-d1 |
16.2-d |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{4} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 7$ |
2B, 7Ns |
$1$ |
\( 1 \) |
$1$ |
$1192.185571$ |
1.04344140 |
\( 6908228743682104 a^{4} - 13274818433086547 a^{3} - 15940534212321925 a^{2} + 30631230136396826 a - 3595022728230192 \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( -41 a^{4} - 18 a^{3} + 227 a^{2} + 55 a - 297\) , \( -241 a^{4} - 11 a^{3} + 1504 a^{2} + 166 a - 2029\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-6a+1\right){x}^{2}+\left(-41a^{4}-18a^{3}+227a^{2}+55a-297\right){x}-241a^{4}-11a^{3}+1504a^{2}+166a-2029$ |
| 16.2-d2 |
16.2-d |
$2$ |
$2$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{8} \) |
$33.67956$ |
$(-a^3+3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 7$ |
2B, 7Ns |
$1$ |
\( 1 \) |
$1$ |
$1192.185571$ |
1.04344140 |
\( -3925017565 a^{4} - 4983392400 a^{3} + 16949294508 a^{2} + 21691981177 a - 3004697106 \) |
\( \bigl[a + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a + 1\) , \( -2 a^{4} + 9 a^{3} + 2 a^{2} - 27 a + 2\) , \( 14 a^{4} - 20 a^{3} - 37 a^{2} + 40 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-6a-2\right){x}^{2}+\left(-2a^{4}+9a^{3}+2a^{2}-27a+2\right){x}+14a^{4}-20a^{3}-37a^{2}+40a-5$ |
| 22.1-a1 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{5} \cdot 11 \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$16$ |
\( 1 \) |
$1$ |
$86.22559564$ |
1.20748123 |
\( -\frac{2436881785253004995}{352} a^{4} - \frac{3147202824593475873}{352} a^{3} + \frac{10556626818408921991}{352} a^{2} + \frac{13633776932551138093}{352} a - \frac{1886844735215910889}{352} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 3\) , \( -19 a^{4} - 60 a^{3} - 36 a^{2} + 20 a + 4\) , \( -437 a^{4} - 1024 a^{3} + 394 a^{2} + 1345 a - 178\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a-2\right){x}^{2}+\left(-19a^{4}-60a^{3}-36a^{2}+20a+4\right){x}-437a^{4}-1024a^{3}+394a^{2}+1345a-178$ |
| 22.1-a2 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{10} \cdot 11^{8} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 2^{4} \) |
$1$ |
$21.55639891$ |
1.20748123 |
\( \frac{1148718540007675210637813}{219503494144} a^{4} - \frac{2155125798813562472945721}{219503494144} a^{3} - \frac{2744420182142965010799985}{219503494144} a^{2} + \frac{4961020353481565935952613}{219503494144} a - \frac{382882715997590265341505}{219503494144} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( 1\) , \( -25 a^{4} - 3 a^{3} + 56 a^{2} - 13 a + 6\) , \( 300 a^{4} + 756 a^{3} - 518 a^{2} - 1388 a + 184\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-25a^{4}-3a^{3}+56a^{2}-13a+6\right){x}+300a^{4}+756a^{3}-518a^{2}-1388a+184$ |
| 22.1-a3 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{10} \cdot 11^{2} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1379.609530$ |
1.20748123 |
\( -\frac{3628139006189}{123904} a^{4} - \frac{4661034067567}{123904} a^{3} + \frac{15710811524105}{123904} a^{2} + \frac{20201587498915}{123904} a - \frac{2796655538087}{123904} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 3\) , \( -4 a^{4} - 5 a^{3} + 4 a^{2} + 4\) , \( -2 a^{4} - 5 a^{3} - a^{2} + a - 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a-2\right){x}^{2}+\left(-4a^{4}-5a^{3}+4a^{2}+4\right){x}-2a^{4}-5a^{3}-a^{2}+a-3$ |
| 22.1-a4 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{2} \cdot 11^{40} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$4$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$4.311279782$ |
1.20748123 |
\( \frac{1101322782303426729856008351776372651264231003053}{1810370222727038072235574241395876818633604} a^{4} - \frac{1690198350885917643327964493312479992666652865717}{1810370222727038072235574241395876818633604} a^{3} - \frac{3965770353897724094461622189053314041673517520285}{1810370222727038072235574241395876818633604} a^{2} + \frac{6070449077744131448544187055612604584686182560697}{1810370222727038072235574241395876818633604} a - \frac{697381859515741055502234476193984986080974013333}{1810370222727038072235574241395876818633604} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a - 1\) , \( a^{4} - 3 a^{2} + a\) , \( -776 a^{4} + 2179 a^{3} + 1315 a^{2} - 5544 a + 664\) , \( -2581 a^{4} - 7124 a^{3} + 13607 a^{2} + 25786 a - 3450\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{4}-3a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-5a-1\right){x}^{2}+\left(-776a^{4}+2179a^{3}+1315a^{2}-5544a+664\right){x}-2581a^{4}-7124a^{3}+13607a^{2}+25786a-3450$ |
| 22.1-a5 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{5} \cdot 11 \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$1379.609530$ |
1.20748123 |
\( \frac{5133891}{352} a^{4} + \frac{1371265}{352} a^{3} - \frac{29420263}{352} a^{2} - \frac{6837869}{352} a + \frac{35504745}{352} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( a^{4} - 5 a^{2} - a + 4\) , \( a^{4} - a^{3} - 3 a^{2} + 4 a + 1\) , \( 4 a^{4} + 6 a^{3} - 10 a^{2} - 10 a + 8\) , \( 11 a^{4} + 21 a^{3} - 22 a^{2} - 37 a + 7\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+4\right){x}^{2}+\left(4a^{4}+6a^{3}-10a^{2}-10a+8\right){x}+11a^{4}+21a^{3}-22a^{2}-37a+7$ |
| 22.1-a6 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{20} \cdot 11^{4} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$689.8047651$ |
1.20748123 |
\( \frac{13229274773910643}{15352201216} a^{4} - \frac{20739047300800335}{15352201216} a^{3} - \frac{37270695561414103}{15352201216} a^{2} + \frac{47299204188218115}{15352201216} a + \frac{9197738213488761}{15352201216} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( 1\) , \( -20 a^{4} - 43 a^{3} + 31 a^{2} + 77 a - 4\) , \( 200 a^{4} + 410 a^{3} - 361 a^{2} - 732 a + 101\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-20a^{4}-43a^{3}+31a^{2}+77a-4\right){x}+200a^{4}+410a^{3}-361a^{2}-732a+101$ |
| 22.1-a7 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{40} \cdot 11^{2} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$344.9023825$ |
1.20748123 |
\( \frac{632989884976858041846779}{133040906960896} a^{4} + \frac{1300243252460380415741321}{133040906960896} a^{3} - \frac{1127122228398216129320895}{133040906960896} a^{2} - \frac{2315280835302866314806261}{133040906960896} a + \frac{308162520326391045149201}{133040906960896} \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -13 a^{4} + 24 a^{3} + 35 a^{2} - 53 a - 7\) , \( -87 a^{4} + 157 a^{3} + 225 a^{2} - 362 a - 5\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-13a^{4}+24a^{3}+35a^{2}-53a-7\right){x}-87a^{4}+157a^{3}+225a^{2}-362a-5$ |
| 22.1-a8 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{4} \cdot 11^{20} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.4.2 |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$137.9609530$ |
1.20748123 |
\( -\frac{25095789757994044241298179142930749}{10763999918920960147216} a^{4} + \frac{38908769324572464615640179971717553}{10763999918920960147216} a^{3} + \frac{90241889718014237259081358838816217}{10763999918920960147216} a^{2} - \frac{139909779212988299755034293057991885}{10763999918920960147216} a + \frac{16183891495459657000014828406219753}{10763999918920960147216} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a - 1\) , \( a^{4} - 3 a^{2} + a\) , \( -451 a^{4} + 1559 a^{3} + 560 a^{2} - 4119 a + 499\) , \( 19331 a^{4} - 49010 a^{3} - 37084 a^{2} + 122273 a - 14762\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{4}-3a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-5a-1\right){x}^{2}+\left(-451a^{4}+1559a^{3}+560a^{2}-4119a+499\right){x}+19331a^{4}-49010a^{3}-37084a^{2}+122273a-14762$ |
| 22.1-a9 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{2} \cdot 11^{10} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$275.9219060$ |
1.20748123 |
\( \frac{209175569528340456184975}{103749698404} a^{4} + \frac{351809974552347599357581}{103749698404} a^{3} - \frac{535749557624336181404395}{103749698404} a^{2} - \frac{646244849688408568222213}{103749698404} a + \frac{388421426694665947082389}{103749698404} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - 3 a^{2} + a\) , \( a^{4} - 4 a^{2} + a + 2\) , \( 1013 a^{4} + 921 a^{3} - 4478 a^{2} - 4490 a + 628\) , \( -34999 a^{4} - 42641 a^{3} + 146840 a^{2} + 178367 a - 24819\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+2\right){y}={x}^{3}+\left(a^{4}-3a^{2}+a\right){x}^{2}+\left(1013a^{4}+921a^{3}-4478a^{2}-4490a+628\right){x}-34999a^{4}-42641a^{3}+146840a^{2}+178367a-24819$ |
| 22.1-a10 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2 \cdot 11^{5} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 5 \) |
$1$ |
$275.9219060$ |
1.20748123 |
\( \frac{346498375995528032618309661505}{322102} a^{4} + \frac{43837134967556791672353986051}{322102} a^{3} - \frac{2073444214388867690985592710423}{322102} a^{2} - \frac{262321154068086150962551780255}{322102} a + \frac{2738799528217201247305524525051}{322102} \) |
\( \bigl[1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 7 a + 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -74 a^{4} + 137 a^{3} + 164 a^{2} - 273 a - 1\) , \( 709 a^{4} - 1437 a^{3} - 1441 a^{2} + 3025 a - 310\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+7a+1\right){x}^{2}+\left(-74a^{4}+137a^{3}+164a^{2}-273a-1\right){x}+709a^{4}-1437a^{3}-1441a^{2}+3025a-310$ |
| 22.1-a11 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{8} \cdot 11^{10} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$68.98047651$ |
1.20748123 |
\( -\frac{230077359927366099516080162197985392229}{6639980697856} a^{4} + \frac{356741063602784265503317564288813681769}{6639980697856} a^{3} + \frac{827327651817715483015823514374299374625}{6639980697856} a^{2} - \frac{1282793519153634038638288814908057372501}{6639980697856} a + \frac{148386593223848581867399741892422147569}{6639980697856} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 4 a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 2\) , \( a^{4} - 3 a^{2} + 1\) , \( -1866 a^{4} + 1781 a^{3} + 7525 a^{2} - 3689 a - 6469\) , \( 229907 a^{4} - 333034 a^{3} - 725889 a^{2} + 743723 a + 328161\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+4a\right){x}{y}+\left(a^{4}-3a^{2}+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-2\right){x}^{2}+\left(-1866a^{4}+1781a^{3}+7525a^{2}-3689a-6469\right){x}+229907a^{4}-333034a^{3}-725889a^{2}+743723a+328161$ |
| 22.1-a12 |
22.1-a |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2 \cdot 11^{5} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$16$ |
\( 5 \) |
$1$ |
$17.24511912$ |
1.20748123 |
\( \frac{18139655468061405760563186954543}{322102} a^{4} + \frac{37260060226221383503463314049375}{322102} a^{3} - \frac{32300362707920099111078740166859}{322102} a^{2} - \frac{66346708204094557347602822221429}{322102} a + \frac{8830733362897992103585812107549}{322102} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - 3 a^{2} + a\) , \( a^{4} - 4 a^{2} + a + 2\) , \( 1368 a^{4} + 511 a^{3} - 8818 a^{2} - 8480 a + 1203\) , \( 6862 a^{4} - 47291 a^{3} - 227594 a^{2} - 199021 a + 28918\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+2\right){y}={x}^{3}+\left(a^{4}-3a^{2}+a\right){x}^{2}+\left(1368a^{4}+511a^{3}-8818a^{2}-8480a+1203\right){x}+6862a^{4}-47291a^{3}-227594a^{2}-199021a+28918$ |
| 22.1-b1 |
22.1-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{16} \cdot 11 \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$174.4460945$ |
2.44289858 |
\( -\frac{1831865193490785685007}{720896} a^{4} - \frac{2365855200321367014757}{720896} a^{3} + \frac{7935687489317182243523}{720896} a^{2} + \frac{10248946039040205873697}{720896} a - \frac{1418400452916131438541}{720896} \) |
\( \bigl[a^{4} - 3 a^{2} + a\) , \( a^{4} - 5 a^{2} - a + 3\) , \( a^{4} - 4 a^{2} + 3\) , \( -57 a^{4} - 143 a^{3} + 81 a^{2} + 264 a - 32\) , \( 769 a^{4} + 1503 a^{3} - 1409 a^{2} - 2633 a + 351\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+3\right){x}^{2}+\left(-57a^{4}-143a^{3}+81a^{2}+264a-32\right){x}+769a^{4}+1503a^{3}-1409a^{2}-2633a+351$ |
| 22.1-b2 |
22.1-b |
$6$ |
$8$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{2} \cdot 11^{2} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2791.137512$ |
2.44289858 |
\( -\frac{411375}{484} a^{4} - \frac{284173}{484} a^{3} + \frac{1837767}{484} a^{2} + \frac{1153613}{484} a - \frac{248041}{484} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( a^{3} - 3 a\) , \( a^{4} - 4 a^{2} + 2\) , \( a^{3} - 3 a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}^{2}+\left(a^{4}-4a^{2}+2\right){x}+a^{3}-3a+1$ |
*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.
