| 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 |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{18} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$64$ |
\( 2 \) |
$1$ |
$11.20325588$ |
1.25571607 |
\( \frac{368220282096876118812818744721291}{64} a^{4} - \frac{999263390585018050007174044270825}{64} a^{3} - \frac{128598577663049307742182854425741}{64} a^{2} + \frac{1325048614540433939777782654403315}{64} a - \frac{429720804565448659899057181182391}{64} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( 283 a^{4} + 479 a^{3} - 1964 a^{2} - 1690 a + 853\) , \( 6417 a^{4} + 8230 a^{3} - 40792 a^{2} - 32420 a + 17481\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(283a^{4}+479a^{3}-1964a^{2}-1690a+853\right){x}+6417a^{4}+8230a^{3}-40792a^{2}-32420a+17481$ |
| 16.2-a2 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$64$ |
\( 2 \) |
$1$ |
$11.20325588$ |
1.25571607 |
\( -\frac{2543764801464067622094722041}{4} a^{4} - \frac{548627770988475867173663789}{4} a^{3} + \frac{12051870661999460674619673615}{4} a^{2} + \frac{7019869609621811006336146559}{4} a - \frac{4184940439198929573320834223}{4} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{4} - 4 a^{2} - a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( -596 a^{4} + 1400 a^{3} + 1428 a^{2} - 3939 a + 1202\) , \( 5779 a^{4} - 11680 a^{3} - 15253 a^{2} + 31913 a - 9250\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-4a^{2}-a+1\right){x}^{2}+\left(-596a^{4}+1400a^{3}+1428a^{2}-3939a+1202\right){x}+5779a^{4}-11680a^{3}-15253a^{2}+31913a-9250$ |
| 16.2-a3 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{24} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$358.5041882$ |
1.25571607 |
\( \frac{2632818763157728469}{4096} a^{4} - \frac{7144835376719340663}{4096} a^{3} - \frac{919502457946488339}{4096} a^{2} + \frac{9474232411249232493}{4096} a - \frac{3072546256788093161}{4096} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( 8 a^{4} + 34 a^{3} - 69 a^{2} - 110 a - 7\) , \( 137 a^{4} + 107 a^{3} - 806 a^{2} - 503 a + 411\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(8a^{4}+34a^{3}-69a^{2}-110a-7\right){x}+137a^{4}+107a^{3}-806a^{2}-503a+411$ |
| 16.2-a4 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{36} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1434.016753$ |
1.25571607 |
\( \frac{114072505235989}{16777216} a^{4} - \frac{309171459975735}{16777216} a^{3} - \frac{39987641649875}{16777216} a^{2} + \frac{409926565809581}{16777216} a - \frac{132882907511593}{16777216} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( 3 a^{4} + 4 a^{3} - 14 a^{2} - 15 a + 3\) , \( -a^{4} + 2 a^{3} + 10 a^{2} + 3 a - 9\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(3a^{4}+4a^{3}-14a^{2}-15a+3\right){x}-a^{4}+2a^{3}+10a^{2}+3a-9$ |
| 16.2-a5 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{24} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$2868.033506$ |
1.25571607 |
\( -\frac{1996365013}{4096} a^{4} - \frac{440220553}{4096} a^{3} + \frac{9470869011}{4096} a^{2} + \frac{5532001683}{4096} a - \frac{3287623447}{4096} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a - 1\) , \( a^{3} - 2 a\) , \( 4 a^{4} - a^{3} - 20 a^{2} + 21\) , \( -a^{4} + 4 a^{3} + 10 a^{2} - 6 a - 12\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+3a\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a^{4}-a^{3}-20a^{2}+21\right){x}-a^{4}+4a^{3}+10a^{2}-6a-12$ |
| 16.2-a6 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{16} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$2868.033506$ |
1.25571607 |
\( \frac{434907}{16} a^{4} - \frac{1241369}{16} a^{3} - \frac{32701}{16} a^{2} + \frac{1668547}{16} a - \frac{641655}{16} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 2\) , \( -a^{3} + 2 a^{2} + 4 a - 3\) , \( a^{3} - 3 a\) , \( -2 a^{4} + 4 a^{3} + 13 a^{2} - 5 a - 10\) , \( 6 a^{4} - 23 a^{2} + 3 a + 21\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-3\right){x}^{2}+\left(-2a^{4}+4a^{3}+13a^{2}-5a-10\right){x}+6a^{4}-23a^{2}+3a+21$ |
| 16.2-a7 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{60} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$89.62604706$ |
1.25571607 |
\( \frac{46634688667323589781}{281474976710656} a^{4} - \frac{28353246678952764855}{281474976710656} a^{3} - \frac{246000524290496779347}{281474976710656} a^{2} + \frac{47096710387511739437}{281474976710656} a + \frac{255702289276942585943}{281474976710656} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - 3 a\) , \( -19 a^{4} + 26 a^{3} + 50 a^{2} - 11 a - 8\) , \( -87 a^{4} + 146 a^{3} + 169 a^{2} - 116 a + 11\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(-19a^{4}+26a^{3}+50a^{2}-11a-8\right){x}-87a^{4}+146a^{3}+169a^{2}-116a+11$ |
| 16.2-a8 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{20} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1434.016753$ |
1.25571607 |
\( \frac{1379657237}{256} a^{4} - \frac{1096285751}{256} a^{3} - \frac{7471095507}{256} a^{2} + \frac{2559257005}{256} a + \frac{8910195159}{256} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{4} - 6 a^{2} - 2 a + 6\) , \( 0\) , \( -2 a^{4} + 6 a^{3} + a^{2} - 9 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(a^{4}-6a^{2}-2a+6\right){x}^{2}+\left(-2a^{4}+6a^{3}+a^{2}-9a+3\right){x}$ |
| 16.2-a9 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{28} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$89.62604706$ |
1.25571607 |
\( -\frac{7559431281060203}{65536} a^{4} + \frac{16188692733137993}{65536} a^{3} + \frac{19327555154480557}{65536} a^{2} - \frac{44739842650069459}{65536} a + \frac{13251346548807255}{65536} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{2} - a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( 22 a^{4} - 38 a^{3} - 47 a^{2} + 55 a - 14\) , \( 47 a^{4} - 65 a^{3} - 147 a^{2} + 127 a - 26\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(22a^{4}-38a^{3}-47a^{2}+55a-14\right){x}+47a^{4}-65a^{3}-147a^{2}+127a-26$ |
| 16.2-a10 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$358.5041882$ |
1.25571607 |
\( \frac{3580510971361285}{16} a^{4} - \frac{2390189577072135}{16} a^{3} - \frac{18818661585251171}{16} a^{2} + \frac{4414105873010333}{16} a + \frac{19919219976060599}{16} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{4} - 4 a^{2} - a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( 169 a^{4} - 365 a^{3} - 437 a^{2} + 1001 a - 298\) , \( 743 a^{4} - 1582 a^{3} - 1903 a^{2} + 4372 a - 1292\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-4a^{2}-a+1\right){x}^{2}+\left(169a^{4}-365a^{3}-437a^{2}+1001a-298\right){x}+743a^{4}-1582a^{3}-1903a^{2}+4372a-1292$ |
| 16.2-a11 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{18} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$89.62604706$ |
1.25571607 |
\( \frac{1796312818174532075637}{64} a^{4} + \frac{2278391536528641048809}{64} a^{3} - \frac{3813436072108364071795}{64} a^{2} - \frac{3261364273074569183987}{64} a + \frac{1583828266902251093431}{64} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( -187 a^{4} + 69 a^{3} + 946 a^{2} - 50 a - 1027\) , \( 2309 a^{4} - 736 a^{3} - 12124 a^{2} + 50 a + 11621\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-187a^{4}+69a^{3}+946a^{2}-50a-1027\right){x}+2309a^{4}-736a^{3}-12124a^{2}+50a+11621$ |
| 16.2-a12 |
16.2-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{14} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$89.62604706$ |
1.25571607 |
\( \frac{1106260209896765075720017449977}{4} a^{4} - \frac{695987117739716713338897632211}{4} a^{3} - \frac{5789418248621984721575448431631}{4} a^{2} + \frac{1171688557315894313385270125441}{4} a + \frac{5965839219757419929153325061103}{4} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{4} - 6 a^{2} - 2 a + 6\) , \( 0\) , \( -422 a^{4} + 286 a^{3} + 2161 a^{2} - 489 a - 2237\) , \( 6514 a^{4} - 3548 a^{3} - 35312 a^{2} + 6188 a + 36728\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(a^{4}-6a^{2}-2a+6\right){x}^{2}+\left(-422a^{4}+286a^{3}+2161a^{2}-489a-2237\right){x}+6514a^{4}-3548a^{3}-35312a^{2}+6188a+36728$ |
| 16.2-b1 |
16.2-b |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{8} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1552.812689$ |
1.35974133 |
\( 358762499 a^{4} - 839089725 a^{3} - 643809485 a^{2} + 1835732071 a - 556242878 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{3} - 2 a - 1\) , \( a^{4} - 5 a^{2} - a + 4\) , \( 3 a^{4} - 4 a^{3} - 7 a^{2} + 12 a - 4\) , \( -2 a^{4} + 6 a^{3} + 7 a^{2} - 15 a + 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+\left(a^{4}-5a^{2}-a+4\right){y}={x}^{3}+\left(a^{3}-2a-1\right){x}^{2}+\left(3a^{4}-4a^{3}-7a^{2}+12a-4\right){x}-2a^{4}+6a^{3}+7a^{2}-15a+1$ |
| 16.2-b2 |
16.2-b |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{8} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1552.812689$ |
1.35974133 |
\( -1775912 a^{4} - 798213 a^{3} + 7383953 a^{2} + 4527695 a - 2623862 \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 1\) , \( a^{4} - 4 a^{2} + 2\) , \( -2 a^{3} - a^{2} + 3 a + 1\) , \( -a^{4} - a^{3} + 2 a^{2} + a - 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-2a^{3}-a^{2}+3a+1\right){x}-a^{4}-a^{3}+2a^{2}+a-1$ |
| 16.2-b3 |
16.2-b |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{4} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1552.812689$ |
1.35974133 |
\( 4217846417445 a^{4} + 5349713818023 a^{3} - 8954188463434 a^{2} - 7657692332285 a + 3718877580798 \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a^{3} - 2 a - 2\) , \( a\) , \( 13 a^{4} - 20 a^{3} - 31 a^{2} + 56 a - 15\) , \( -18 a^{4} + 53 a^{3} + 45 a^{2} - 136 a + 43\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+3a\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-2a-2\right){x}^{2}+\left(13a^{4}-20a^{3}-31a^{2}+56a-15\right){x}-18a^{4}+53a^{3}+45a^{2}-136a+43$ |
| 16.2-b4 |
16.2-b |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{4} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1552.812689$ |
1.35974133 |
\( -383866242875132341 a^{4} + 821906963243723177 a^{3} + 981429731922769491 a^{2} - 2271536193148794877 a + 672783536171615834 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 4\) , \( a^{3} - 3 a\) , \( 3 a^{4} - 3 a^{3} - 18 a^{2} + 4 a + 9\) , \( -12 a^{4} - 4 a^{3} + 40 a^{2} + 17 a - 15\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a-4\right){x}^{2}+\left(3a^{4}-3a^{3}-18a^{2}+4a+9\right){x}-12a^{4}-4a^{3}+40a^{2}+17a-15$ |
| 16.2-c1 |
16.2-c |
$2$ |
$2$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$33.66304$ |
$(a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.022760314$ |
$12035.72375$ |
2.39876501 |
\( 587530 a^{4} - 1258841 a^{3} - 1500968 a^{2} + 3479072 a - 1030860 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{4} - 4 a^{2} - 2 a + 1\) , \( a^{2} + a - 2\) , \( 8 a^{4} - 19 a^{3} - 19 a^{2} + 54 a - 16\) , \( -24 a^{4} + 50 a^{3} + 62 a^{2} - 138 a + 40\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}-4a^{2}-2a+1\right){x}^{2}+\left(8a^{4}-19a^{3}-19a^{2}+54a-16\right){x}-24a^{4}+50a^{3}+62a^{2}-138a+40$ |
| 16.2-c2 |
16.2-c |
$2$ |
$2$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$33.66304$ |
$(a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.045520629$ |
$6017.861877$ |
2.39876501 |
\( -2403655604077 a^{4} + 5146535696608 a^{3} + 6145419251688 a^{2} - 14223680620576 a + 4212769815616 \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 6 a - 2\) , \( a^{4} - 4 a^{2} - a + 2\) , \( -3 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 2\) , \( a^{3} - 2 a^{2} - 4 a + 4\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-4a^{2}-a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+6a-2\right){x}^{2}+\left(-3a^{4}+2a^{3}+9a^{2}-7a-2\right){x}+a^{3}-2a^{2}-4a+4$ |
| 16.2-d1 |
16.2-d |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{14} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$922.0911311$ |
1.61488302 |
\( -\frac{174633257}{4} a^{4} + \frac{45165843}{4} a^{3} + \frac{876009235}{4} a^{2} + \frac{107458075}{4} a - \frac{654862103}{4} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - 2 a\) , \( 31 a^{4} + 7 a^{3} - 148 a^{2} - 89 a + 50\) , \( -231 a^{4} - 50 a^{3} + 1093 a^{2} + 636 a - 380\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(31a^{4}+7a^{3}-148a^{2}-89a+50\right){x}-231a^{4}-50a^{3}+1093a^{2}+636a-380$ |
| 16.2-d2 |
16.2-d |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{18} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$922.0911311$ |
1.61488302 |
\( \frac{264059}{64} a^{4} - \frac{1783929}{64} a^{3} + \frac{447267}{64} a^{2} + \frac{2436259}{64} a - \frac{883495}{64} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 6 a\) , \( a^{2} + a - 2\) , \( -a^{4} + 5 a^{3} - 5 a + 3\) , \( 3 a^{4} - 4 a^{3} - 3 a^{2} + 6 a - 2\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+6a\right){x}^{2}+\left(-a^{4}+5a^{3}-5a+3\right){x}+3a^{4}-4a^{3}-3a^{2}+6a-2$ |
| 16.2-d3 |
16.2-d |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{24} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$461.0455655$ |
1.61488302 |
\( \frac{1772935448181}{4096} a^{4} + \frac{2248341026729}{4096} a^{3} - \frac{3764435351923}{4096} a^{2} - \frac{3218299789555}{4096} a + \frac{1564113583863}{4096} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( -9 a^{4} + 6 a^{3} + 48 a^{2} - 9 a - 49\) , \( -20 a^{4} + 12 a^{3} + 107 a^{2} - 20 a - 111\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-9a^{4}+6a^{3}+48a^{2}-9a-49\right){x}-20a^{4}+12a^{3}+107a^{2}-20a-111$ |
| 16.2-d4 |
16.2-d |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$33.66304$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$461.0455655$ |
1.61488302 |
\( \frac{48597558931232101}{16} a^{4} - \frac{30574429654392887}{16} a^{3} - \frac{254326777735306691}{16} a^{2} + \frac{51471799486964365}{16} a + \frac{262076878907551607}{16} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 4\) , \( a^{4} - 4 a^{2} + 2\) , \( 25 a^{4} - 118 a^{2} - 52 a + 49\) , \( -88 a^{4} + 382 a^{2} + 203 a - 117\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+4\right){x}^{2}+\left(25a^{4}-118a^{2}-52a+49\right){x}-88a^{4}+382a^{2}+203a-117$ |
*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.
