| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 16.2-a1 |
16.2-a |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$39.42603362$ |
2.56982456 |
\( -\frac{49614921476871042165389200041}{16} a^{4} + \frac{4728102009895627655218150011}{2} a^{3} + \frac{61318224529309629403565987533}{4} a^{2} + \frac{55483041245914317421631499803}{16} a - \frac{80177163286129881264229188029}{16} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 2 a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a\) , \( -3354 a^{4} + 4787 a^{3} + 15356 a^{2} - 8849 a - 13857\) , \( 151078 a^{4} - 218478 a^{3} - 696616 a^{2} + 402246 a + 628666\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+2a\right){x}^{2}+\left(-3354a^{4}+4787a^{3}+15356a^{2}-8849a-13857\right){x}+151078a^{4}-218478a^{3}-696616a^{2}+402246a+628666$ |
| 16.2-a2 |
16.2-a |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{22} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1971.301681$ |
2.56982456 |
\( \frac{643897}{1024} a^{4} - \frac{102985}{128} a^{3} - \frac{650445}{256} a^{2} + \frac{1528149}{1024} a + \frac{1961773}{1024} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( 0\) , \( -2 a^{4} + 4 a^{3} + 7 a^{2} - 8 a - 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(-2a^{4}+4a^{3}+7a^{2}-8a-3\right){x}$ |
| 16.2-a3 |
16.2-a |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{32} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$985.6508406$ |
2.56982456 |
\( -\frac{202755819017}{1048576} a^{4} + \frac{52665021849}{131072} a^{3} + \frac{143828793821}{262144} a^{2} - \frac{735606334693}{1048576} a + \frac{186325767619}{1048576} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a\) , \( -10 a^{4} + 41 a^{3} - 21 a^{2} - 42 a + 24\) , \( -37 a^{4} + 137 a^{3} - 56 a^{2} - 114 a + 51\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+3a\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-6a-1\right){x}^{2}+\left(-10a^{4}+41a^{3}-21a^{2}-42a+24\right){x}-37a^{4}+137a^{3}-56a^{2}-114a+51$ |
| 16.2-a4 |
16.2-a |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$78.85206725$ |
2.56982456 |
\( \frac{67414803450012505}{4} a^{4} + 11415196857224997 a^{3} - 36805012364856254 a^{2} - \frac{56720491743749963}{4} a + \frac{50406441290652989}{4} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( 0\) , \( -372 a^{4} + 569 a^{3} + 1747 a^{2} - 1093 a - 1673\) , \( 6663 a^{4} - 10082 a^{3} - 31276 a^{2} + 18198 a + 28116\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(-372a^{4}+569a^{3}+1747a^{2}-1093a-1673\right){x}+6663a^{4}-10082a^{3}-31276a^{2}+18198a+28116$ |
| 16.2-b1 |
16.2-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$31.88092791$ |
2.07802774 |
\( -\frac{49614921476871042165389200041}{16} a^{4} + \frac{4728102009895627655218150011}{2} a^{3} + \frac{61318224529309629403565987533}{4} a^{2} + \frac{55483041245914317421631499803}{16} a - \frac{80177163286129881264229188029}{16} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( -1447 a^{4} + 2134 a^{3} + 6919 a^{2} - 3800 a - 6557\) , \( -48380 a^{4} + 74581 a^{3} + 226206 a^{2} - 137355 a - 204333\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+2a-1\right){x}^{2}+\left(-1447a^{4}+2134a^{3}+6919a^{2}-3800a-6557\right){x}-48380a^{4}+74581a^{3}+226206a^{2}-137355a-204333$ |
| 16.2-b2 |
16.2-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{22} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1594.046395$ |
2.07802774 |
\( \frac{643897}{1024} a^{4} - \frac{102985}{128} a^{3} - \frac{650445}{256} a^{2} + \frac{1528149}{1024} a + \frac{1961773}{1024} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + 3 a^{2} + a - 6\) , \( a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( a^{4} - 4 a^{3} - 5 a^{2} + 6 a + 5\) , \( -6 a^{4} - 2 a^{3} + 16 a^{2} + a - 9\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+4\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+a-6\right){x}^{2}+\left(a^{4}-4a^{3}-5a^{2}+6a+5\right){x}-6a^{4}-2a^{3}+16a^{2}+a-9$ |
| 16.2-b3 |
16.2-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{32} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$797.0231977$ |
2.07802774 |
\( -\frac{202755819017}{1048576} a^{4} + \frac{52665021849}{131072} a^{3} + \frac{143828793821}{262144} a^{2} - \frac{735606334693}{1048576} a + \frac{186325767619}{1048576} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( 62 a^{4} - 47 a^{3} - 311 a^{2} - 61 a + 111\) , \( -420 a^{4} + 324 a^{3} + 2065 a^{2} + 470 a - 669\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){x}^{2}+\left(62a^{4}-47a^{3}-311a^{2}-61a+111\right){x}-420a^{4}+324a^{3}+2065a^{2}+470a-669$ |
| 16.2-b4 |
16.2-b |
$4$ |
$10$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$63.76185582$ |
2.07802774 |
\( \frac{67414803450012505}{4} a^{4} + 11415196857224997 a^{3} - 36805012364856254 a^{2} - \frac{56720491743749963}{4} a + \frac{50406441290652989}{4} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 4\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 4\) , \( a\) , \( 77 a^{4} - 450 a^{3} + 429 a^{2} + 1110 a - 1387\) , \( -8862 a^{4} + 22771 a^{3} + 19927 a^{2} - 49652 a + 8625\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+4\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-4\right){x}^{2}+\left(77a^{4}-450a^{3}+429a^{2}+1110a-1387\right){x}-8862a^{4}+22771a^{3}+19927a^{2}-49652a+8625$ |
| 16.2-c1 |
16.2-c |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1317.172196$ |
1.71708952 |
\( \frac{38612253}{4} a^{4} - 17189978 a^{3} - 39860096 a^{2} + \frac{134107665}{4} a + \frac{118005317}{4} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4\) , \( a^{3} - 3 a^{2} - a + 5\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( -a^{4} + a^{3} + 5 a^{2} - 4\) , \( -7 a^{4} + 10 a^{3} + 34 a^{2} - 16 a - 33\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4\right){x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+5\right){x}^{2}+\left(-a^{4}+a^{3}+5a^{2}-4\right){x}-7a^{4}+10a^{3}+34a^{2}-16a-33$ |
| 16.2-c2 |
16.2-c |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$658.5860982$ |
1.71708952 |
\( -\frac{347407763279705}{16} a^{4} + \frac{123559579559993}{2} a^{3} + \frac{138519839322317}{4} a^{2} - \frac{2205397840702053}{16} a + \frac{821982547313539}{16} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( 19 a^{4} - 47 a^{3} - 30 a^{2} + 107 a - 40\) , \( -44 a^{4} + 128 a^{3} + 72 a^{2} - 284 a + 103\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(19a^{4}-47a^{3}-30a^{2}+107a-40\right){x}-44a^{4}+128a^{3}+72a^{2}-284a+103$ |
| 16.2-d1 |
16.2-d |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.034764318$ |
$12067.76533$ |
2.73451915 |
\( 6138 a^{4} - 15497 a^{3} - 12876 a^{2} + 34148 a - 7508 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2\) , \( -a^{3} + 3 a^{2} + 3 a - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( -a^{4} + a^{3} + 4 a^{2} - a\) , \( -4 a^{3} + 7 a^{2} + 3 a - 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-4\right){x}^{2}+\left(-a^{4}+a^{3}+4a^{2}-a\right){x}-4a^{3}+7a^{2}+3a-3$ |
| 16.2-d2 |
16.2-d |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.069528637$ |
$24135.53067$ |
2.73451915 |
\( -170446532 a^{4} + 491019891 a^{3} + 270844928 a^{2} - 1094370175 a + 408646686 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 8 a^{4} - 7 a^{3} - 38 a^{2} - 4 a + 13\) , \( -17 a^{4} + 13 a^{3} + 85 a^{2} + 20 a - 28\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-3\right){x}^{2}+\left(8a^{4}-7a^{3}-38a^{2}-4a+13\right){x}-17a^{4}+13a^{3}+85a^{2}+20a-28$ |
| 16.2-d3 |
16.2-d |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{10} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.034764318$ |
$6033.882669$ |
2.73451915 |
\( 139855256235025 a^{4} + 94995663763607 a^{3} - 304902051913729 a^{2} - 117631938280982 a + 104398850322924 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 18 a^{4} - 12 a^{3} - 93 a^{2} - 29 a + 23\) , \( 80 a^{4} - 69 a^{3} - 390 a^{2} - 56 a + 148\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-3\right){x}^{2}+\left(18a^{4}-12a^{3}-93a^{2}-29a+23\right){x}+80a^{4}-69a^{3}-390a^{2}-56a+148$ |
| 16.2-d4 |
16.2-d |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{4} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.139057275$ |
$6033.882669$ |
2.73451915 |
\( -196899167397644501 a^{4} + 560235687430537097 a^{3} + 314033749390697041 a^{2} - 1249946151122266014 a + 465872371548084688 \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{4} - a^{3} - 5 a^{2} - a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( a^{4} - 14 a^{2} - 9 a + 14\) , \( 4 a^{3} + 12 a^{2} + 24 a + 22\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+4\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}-a+3\right){x}^{2}+\left(a^{4}-14a^{2}-9a+14\right){x}+4a^{3}+12a^{2}+24a+22$ |
| 16.2-e1 |
16.2-e |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$858.3899466$ |
1.11901267 |
\( \frac{38612253}{4} a^{4} - 17189978 a^{3} - 39860096 a^{2} + \frac{134107665}{4} a + \frac{118005317}{4} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} - a + 2\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -10 a^{4} + 13 a^{3} + 45 a^{2} - 15 a - 29\) , \( 7 a^{4} - 15 a^{3} - 31 a^{2} + 39 a + 38\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}-a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-10a^{4}+13a^{3}+45a^{2}-15a-29\right){x}+7a^{4}-15a^{3}-31a^{2}+39a+38$ |
| 16.2-e2 |
16.2-e |
$2$ |
$2$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$45.22413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$429.1949733$ |
1.11901267 |
\( -\frac{347407763279705}{16} a^{4} + \frac{123559579559993}{2} a^{3} + \frac{138519839322317}{4} a^{2} - \frac{2205397840702053}{16} a + \frac{821982547313539}{16} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 2 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 843 a^{4} - 2398 a^{3} - 1343 a^{2} + 5345 a - 1993\) , \( 23570 a^{4} - 67063 a^{3} - 37590 a^{2} + 149620 a - 55765\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+2a\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+3a\right){x}^{2}+\left(843a^{4}-2398a^{3}-1343a^{2}+5345a-1993\right){x}+23570a^{4}-67063a^{3}-37590a^{2}+149620a-55765$ |
| 16.2-f1 |
16.2-f |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.749829510$ |
$2128.194857$ |
2.60036501 |
\( 6138 a^{4} - 15497 a^{3} - 12876 a^{2} + 34148 a - 7508 \) |
\( \bigl[a\) , \( a^{4} - a^{3} - 5 a^{2} + 3\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( -2 a^{3} + 3 a^{2} + 7 a - 3\) , \( 3 a^{4} - 7 a^{3} - 7 a^{2} + 13 a - 5\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3\right){x}^{2}+\left(-2a^{3}+3a^{2}+7a-3\right){x}+3a^{4}-7a^{3}-7a^{2}+13a-5$ |
| 16.2-f2 |
16.2-f |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.499659021$ |
$1064.097428$ |
2.60036501 |
\( -170446532 a^{4} + 491019891 a^{3} + 270844928 a^{2} - 1094370175 a + 408646686 \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a\) , \( -a^{4} + 3 a^{3} + a^{2} - 7 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 4\) , \( 34 a^{4} - 92 a^{3} - 59 a^{2} + 202 a - 75\) , \( 319 a^{4} - 903 a^{3} - 513 a^{2} + 2011 a - 750\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+3a\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+a^{2}-7a+3\right){x}^{2}+\left(34a^{4}-92a^{3}-59a^{2}+202a-75\right){x}+319a^{4}-903a^{3}-513a^{2}+2011a-750$ |
| 16.2-f3 |
16.2-f |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{10} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.749829510$ |
$266.0243571$ |
2.60036501 |
\( 139855256235025 a^{4} + 94995663763607 a^{3} - 304902051913729 a^{2} - 117631938280982 a + 104398850322924 \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a\) , \( -a^{4} + 3 a^{3} + a^{2} - 7 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 4\) , \( 34 a^{4} - 87 a^{3} - 69 a^{2} + 192 a - 75\) , \( 308 a^{4} - 894 a^{3} - 455 a^{2} + 2006 a - 768\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+3a\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+a^{2}-7a+3\right){x}^{2}+\left(34a^{4}-87a^{3}-69a^{2}+192a-75\right){x}+308a^{4}-894a^{3}-455a^{2}+2006a-768$ |
| 16.2-f4 |
16.2-f |
$4$ |
$4$ |
5.5.147109.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{4} \) |
$45.22413$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$2.999318042$ |
$66.50608928$ |
2.60036501 |
\( -196899167397644501 a^{4} + 560235687430537097 a^{3} + 314033749390697041 a^{2} - 1249946151122266014 a + 465872371548084688 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2\) , \( a^{2} - 2\) , \( a^{2} - a - 2\) , \( 10 a^{4} - 22 a^{3} - 23 a^{2} + 48 a - 11\) , \( 17 a^{4} - 45 a^{3} - 24 a^{2} + 100 a - 50\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(10a^{4}-22a^{3}-23a^{2}+48a-11\right){x}+17a^{4}-45a^{3}-24a^{2}+100a-50$ |
*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.
