| 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 |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{6} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$256$ |
\( 2 \cdot 3 \) |
$1$ |
$1.156294534$ |
1.55523820 |
\( \frac{368220282096876118812818744721291}{64} a^{4} - \frac{999263390585018050007174044270825}{64} a^{3} - \frac{128598577663049307742182854425741}{64} a^{2} + \frac{1325048614540433939777782654403315}{64} a - \frac{429720804565448659899057181182391}{64} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 323 a^{4} - 512 a^{3} - 1014 a^{2} + 1236 a - 293\) , \( 5186 a^{4} - 9226 a^{3} - 15116 a^{2} + 23632 a - 6313\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}^{2}+\left(323a^{4}-512a^{3}-1014a^{2}+1236a-293\right){x}+5186a^{4}-9226a^{3}-15116a^{2}+23632a-6313$ |
| 2.1-a2 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$256$ |
\( 2 \) |
$1$ |
$3.468883603$ |
1.55523820 |
\( -\frac{2543764801464067622094722041}{4} a^{4} - \frac{548627770988475867173663789}{4} a^{3} + \frac{12051870661999460674619673615}{4} a^{2} + \frac{7019869609621811006336146559}{4} a - \frac{4184940439198929573320834223}{4} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 3\) , \( a^{3} - 2 a - 1\) , \( -71 a^{4} + 217 a^{3} + 121 a^{2} - 634 a + 207\) , \( -301 a^{4} + 906 a^{3} + 472 a^{2} - 2707 a + 893\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-2a-1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-71a^{4}+217a^{3}+121a^{2}-634a+207\right){x}-301a^{4}+906a^{3}+472a^{2}-2707a+893$ |
| 2.1-a3 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{12} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$37.00142510$ |
1.55523820 |
\( \frac{2632818763157728469}{4096} a^{4} - \frac{7144835376719340663}{4096} a^{3} - \frac{919502457946488339}{4096} a^{2} + \frac{9474232411249232493}{4096} a - \frac{3072546256788093161}{4096} \) |
\( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -13 a^{4} + 55 a^{3} + 20 a^{2} - 116 a - 52\) , \( -71 a^{4} + 256 a^{3} + 73 a^{2} - 511 a - 178\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+3a\right){x}^{2}+\left(-13a^{4}+55a^{3}+20a^{2}-116a-52\right){x}-71a^{4}+256a^{3}+73a^{2}-511a-178$ |
| 2.1-a4 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{24} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1184.045603$ |
1.55523820 |
\( \frac{114072505235989}{16777216} a^{4} - \frac{309171459975735}{16777216} a^{3} - \frac{39987641649875}{16777216} a^{2} + \frac{409926565809581}{16777216} a - \frac{132882907511593}{16777216} \) |
\( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 2 a^{4} + 10 a^{3} - 5 a^{2} - 21 a - 2\) , \( 6 a^{4} + 13 a^{3} - 14 a^{2} - 16 a + 8\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+3a\right){x}^{2}+\left(2a^{4}+10a^{3}-5a^{2}-21a-2\right){x}+6a^{4}+13a^{3}-14a^{2}-16a+8$ |
| 2.1-a5 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{12} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2368.091206$ |
1.55523820 |
\( -\frac{1996365013}{4096} a^{4} - \frac{440220553}{4096} a^{3} + \frac{9470869011}{4096} a^{2} + \frac{5532001683}{4096} a - \frac{3287623447}{4096} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( a^{3} - 2 a\) , \( a^{2} - 2\) , \( 7 a^{4} - 3 a^{3} - 35 a^{2} + 5 a + 35\) , \( 7 a^{4} - 4 a^{3} - 36 a^{2} + 7 a + 37\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-2a\right){x}^{2}+\left(7a^{4}-3a^{3}-35a^{2}+5a+35\right){x}+7a^{4}-4a^{3}-36a^{2}+7a+37$ |
| 2.1-a6 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{4} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$7104.273620$ |
1.55523820 |
\( \frac{434907}{16} a^{4} - \frac{1241369}{16} a^{3} - \frac{32701}{16} a^{2} + \frac{1668547}{16} a - \frac{641655}{16} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( -4 a^{4} + 3 a^{3} + 19 a^{2} - 5 a - 13\) , \( -10 a^{4} + 5 a^{3} + 53 a^{2} - 6 a - 55\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+6a+2\right){x}^{2}+\left(-4a^{4}+3a^{3}+19a^{2}-5a-13\right){x}-10a^{4}+5a^{3}+53a^{2}-6a-55$ |
| 2.1-a7 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{48} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$592.0228016$ |
1.55523820 |
\( \frac{46634688667323589781}{281474976710656} a^{4} - \frac{28353246678952764855}{281474976710656} a^{3} - \frac{246000524290496779347}{281474976710656} a^{2} + \frac{47096710387511739437}{281474976710656} a + \frac{255702289276942585943}{281474976710656} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( a^{2} + a - 2\) , \( -2 a^{4} - 4 a^{3} + 6 a^{2} + 12 a - 1\) , \( -2 a^{4} - a^{3} + 8 a^{2} + 5 a - 5\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-6a-2\right){x}^{2}+\left(-2a^{4}-4a^{3}+6a^{2}+12a-1\right){x}-2a^{4}-a^{3}+8a^{2}+5a-5$ |
| 2.1-a8 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{8} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$3552.136810$ |
1.55523820 |
\( \frac{1379657237}{256} a^{4} - \frac{1096285751}{256} a^{3} - \frac{7471095507}{256} a^{2} + \frac{2559257005}{256} a + \frac{8910195159}{256} \) |
\( \bigl[a^{3} - 3 a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{4} - 4 a^{2} - a + 1\) , \( -5 a^{4} + 10 a^{3} + 11 a^{2} - 18 a - 8\) , \( -3 a^{4} + a^{3} + 18 a^{2} - 4 a - 21\bigr] \) |
${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(a^{4}-4a^{2}-a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(-5a^{4}+10a^{3}+11a^{2}-18a-8\right){x}-3a^{4}+a^{3}+18a^{2}-4a-21$ |
| 2.1-a9 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{16} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$1776.068405$ |
1.55523820 |
\( -\frac{7559431281060203}{65536} a^{4} + \frac{16188692733137993}{65536} a^{3} + \frac{19327555154480557}{65536} a^{2} - \frac{44739842650069459}{65536} a + \frac{13251346548807255}{65536} \) |
\( \bigl[a^{2} - 1\) , \( -1\) , \( a^{3} - 3 a - 1\) , \( 18 a^{4} - 40 a^{3} - 21 a^{2} + 48 a - 15\) , \( 13 a^{4} - 15 a^{3} - 33 a^{2} - 3 a + 5\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}-{x}^{2}+\left(18a^{4}-40a^{3}-21a^{2}+48a-15\right){x}+13a^{4}-15a^{3}-33a^{2}-3a+5$ |
| 2.1-a10 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$111.0042753$ |
1.55523820 |
\( \frac{3580510971361285}{16} a^{4} - \frac{2390189577072135}{16} a^{3} - \frac{18818661585251171}{16} a^{2} + \frac{4414105873010333}{16} a + \frac{19919219976060599}{16} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 3\) , \( a^{3} - 2 a - 1\) , \( 24 a^{4} - 53 a^{3} - 64 a^{2} + 141 a - 43\) , \( -17 a^{4} + 35 a^{3} + 40 a^{2} - 101 a + 25\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-2a-1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(24a^{4}-53a^{3}-64a^{2}+141a-43\right){x}-17a^{4}+35a^{3}+40a^{2}-101a+25$ |
| 2.1-a11 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$256$ |
\( 2 \cdot 3 \) |
$1$ |
$1.156294534$ |
1.55523820 |
\( \frac{1796312818174532075637}{64} a^{4} + \frac{2278391536528641048809}{64} a^{3} - \frac{3813436072108364071795}{64} a^{2} - \frac{3261364273074569183987}{64} a + \frac{1583828266902251093431}{64} \) |
\( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -298 a^{4} + 205 a^{3} + 1495 a^{2} - 321 a - 1522\) , \( -4134 a^{4} + 2794 a^{3} + 21224 a^{2} - 5062 a - 22276\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+3a\right){x}^{2}+\left(-298a^{4}+205a^{3}+1495a^{2}-321a-1522\right){x}-4134a^{4}+2794a^{3}+21224a^{2}-5062a-22276$ |
| 2.1-a12 |
2.1-a |
$12$ |
$24$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$27.34288$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$256$ |
\( 2 \) |
$1$ |
$3.468883603$ |
1.55523820 |
\( \frac{1106260209896765075720017449977}{4} a^{4} - \frac{695987117739716713338897632211}{4} a^{3} - \frac{5789418248621984721575448431631}{4} a^{2} + \frac{1171688557315894313385270125441}{4} a + \frac{5965839219757419929153325061103}{4} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 3\) , \( a^{3} - 2 a - 1\) , \( 199 a^{4} - 483 a^{3} - 489 a^{2} + 1316 a - 453\) , \( 3395 a^{4} - 7628 a^{3} - 8616 a^{2} + 20957 a - 6467\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-2a-1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(199a^{4}-483a^{3}-489a^{2}+1316a-453\right){x}+3395a^{4}-7628a^{3}-8616a^{2}+20957a-6467$ |
| 2.1-b1 |
2.1-b |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$27.34288$ |
$(a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.018823955$ |
$6270.128248$ |
1.03353343 |
\( -\frac{174633257}{4} a^{4} + \frac{45165843}{4} a^{3} + \frac{876009235}{4} a^{2} + \frac{107458075}{4} a - \frac{654862103}{4} \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( 19 a^{4} + 5 a^{3} - 89 a^{2} - 53 a + 31\) , \( -71 a^{4} - 15 a^{3} + 338 a^{2} + 199 a - 115\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a-3\right){x}^{2}+\left(19a^{4}+5a^{3}-89a^{2}-53a+31\right){x}-71a^{4}-15a^{3}+338a^{2}+199a-115$ |
| 2.1-b2 |
2.1-b |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{6} \) |
$27.34288$ |
$(a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.006274651$ |
$18810.38474$ |
1.03353343 |
\( \frac{264059}{64} a^{4} - \frac{1783929}{64} a^{3} + \frac{447267}{64} a^{2} + \frac{2436259}{64} a - \frac{883495}{64} \) |
\( \bigl[a^{4} - 5 a^{2} + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{2} + a - 1\) , \( -2 a^{4} + 7 a^{3} - 3 a^{2} - 9 a + 9\) , \( 6 a^{4} - 15 a^{3} - 5 a^{2} + 20 a - 4\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}^{2}+\left(-2a^{4}+7a^{3}-3a^{2}-9a+9\right){x}+6a^{4}-15a^{3}-5a^{2}+20a-4$ |
| 2.1-b3 |
2.1-b |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{12} \) |
$27.34288$ |
$(a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.012549303$ |
$9405.192372$ |
1.03353343 |
\( \frac{1772935448181}{4096} a^{4} + \frac{2248341026729}{4096} a^{3} - \frac{3764435351923}{4096} a^{2} - \frac{3218299789555}{4096} a + \frac{1564113583863}{4096} \) |
\( \bigl[a^{2} - 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 6 a + 2\) , \( 1\) , \( -17 a^{4} + 14 a^{3} + 82 a^{2} - 28 a - 74\) , \( 45 a^{4} - 27 a^{3} - 237 a^{2} + 41 a + 250\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-6a+2\right){x}^{2}+\left(-17a^{4}+14a^{3}+82a^{2}-28a-74\right){x}+45a^{4}-27a^{3}-237a^{2}+41a+250$ |
| 2.1-b4 |
2.1-b |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$27.34288$ |
$(a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.037647910$ |
$3135.064124$ |
1.03353343 |
\( \frac{48597558931232101}{16} a^{4} - \frac{30574429654392887}{16} a^{3} - \frac{254326777735306691}{16} a^{2} + \frac{51471799486964365}{16} a + \frac{262076878907551607}{16} \) |
\( \bigl[1\) , \( -a^{2} - a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( 13 a^{4} + 2 a^{3} - 58 a^{2} - 36 a + 18\) , \( -63 a^{4} + 24 a^{3} + 242 a^{2} + 91 a - 70\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(13a^{4}+2a^{3}-58a^{2}-36a+18\right){x}-63a^{4}+24a^{3}+242a^{2}+91a-70$ |
| 4.1-a1 |
4.1-a |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$29.30538$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$447.2294659$ |
1.17486750 |
\( 358762499 a^{4} - 839089725 a^{3} - 643809485 a^{2} + 1835732071 a - 556242878 \) |
\( \bigl[a\) , \( -a^{4} + 6 a^{2} - 6\) , \( a^{4} - 5 a^{2} - a + 4\) , \( 2 a^{4} - 2 a^{3} - 10 a^{2} + 5 a + 8\) , \( -a^{4} + 3 a^{3} + 4 a^{2} - 3 a - 7\bigr] \) |
${y}^2+a{x}{y}+\left(a^{4}-5a^{2}-a+4\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-6\right){x}^{2}+\left(2a^{4}-2a^{3}-10a^{2}+5a+8\right){x}-a^{4}+3a^{3}+4a^{2}-3a-7$ |
| 4.1-a2 |
4.1-a |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$29.30538$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1341.688397$ |
1.17486750 |
\( -1775912 a^{4} - 798213 a^{3} + 7383953 a^{2} + 4527695 a - 2623862 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( a^{2} + a - 2\) , \( 7 a^{4} - 10 a^{3} - 27 a^{2} + 24 a + 9\) , \( 15 a^{4} - 29 a^{3} - 44 a^{2} + 77 a - 14\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}^{2}+\left(7a^{4}-10a^{3}-27a^{2}+24a+9\right){x}+15a^{4}-29a^{3}-44a^{2}+77a-14$ |
| 4.1-a3 |
4.1-a |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{4} \) |
$29.30538$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1341.688397$ |
1.17486750 |
\( 4217846417445 a^{4} + 5349713818023 a^{3} - 8954188463434 a^{2} - 7657692332285 a + 3718877580798 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -7 a^{4} - a^{3} + 35 a^{2} + 3 a - 34\) , \( -8 a^{4} + 10 a^{3} + 50 a^{2} - 13 a - 57\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-1\right){x}^{2}+\left(-7a^{4}-a^{3}+35a^{2}+3a-34\right){x}-8a^{4}+10a^{3}+50a^{2}-13a-57$ |
| 4.1-a4 |
4.1-a |
$4$ |
$6$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{4} \) |
$29.30538$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$447.2294659$ |
1.17486750 |
\( -383866242875132341 a^{4} + 821906963243723177 a^{3} + 981429731922769491 a^{2} - 2271536193148794877 a + 672783536171615834 \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( a^{4} - 5 a^{2} + 4\) , \( 4 a^{4} - 10 a^{3} - 2 a^{2} + 28 a - 32\) , \( 16 a^{4} - 39 a^{3} - 36 a^{2} + 116 a - 31\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+3a\right){x}{y}+\left(a^{4}-5a^{2}+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){x}^{2}+\left(4a^{4}-10a^{3}-2a^{2}+28a-32\right){x}+16a^{4}-39a^{3}-36a^{2}+116a-31$ |
| 8.1-a1 |
8.1-a |
$2$ |
$2$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$31.40873$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$831.3845321$ |
1.45602611 |
\( 587530 a^{4} - 1258841 a^{3} - 1500968 a^{2} + 3479072 a - 1030860 \) |
\( \bigl[a^{4} - 5 a^{2} + 4\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a\) , \( 0\) , \( 3 a^{3} - 7 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+4\right){x}{y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-5a\right){x}^{2}+\left(3a^{3}-7a+3\right){x}$ |
| 8.1-a2 |
8.1-a |
$2$ |
$2$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$31.40873$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$415.6922660$ |
1.45602611 |
\( -2403655604077 a^{4} + 5146535696608 a^{3} + 6145419251688 a^{2} - 14223680620576 a + 4212769815616 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{3} - 2 a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( 21 a^{4} - 46 a^{3} - 50 a^{2} + 130 a - 40\) , \( 119 a^{4} - 252 a^{3} - 305 a^{2} + 697 a - 206\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a\right){y}={x}^{3}+\left(a^{3}-2a-1\right){x}^{2}+\left(21a^{4}-46a^{3}-50a^{2}+130a-40\right){x}+119a^{4}-252a^{3}-305a^{2}+697a-206$ |
| 9.1-a1 |
9.1-a |
$2$ |
$3$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$31.78086$ |
$(a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.005353504$ |
$18888.18572$ |
1.77090657 |
\( -53060 a^{4} + \frac{432928}{3} a^{3} + 15463 a^{2} - \frac{565285}{3} a + \frac{188426}{3} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{4} + 5 a^{2} + a - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( -a^{4} + 2 a^{3} + a^{2} - 2 a + 2\) , \( -2 a^{3} + 4 a^{2} + 3 a - 5\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+a-4\right){x}^{2}+\left(-a^{4}+2a^{3}+a^{2}-2a+2\right){x}-2a^{3}+4a^{2}+3a-5$ |
| 9.1-a2 |
9.1-a |
$2$ |
$3$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$31.78086$ |
$(a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.016060513$ |
$6296.061908$ |
1.77090657 |
\( \frac{286946845}{27} a^{4} + \frac{61919467}{27} a^{3} - \frac{1359497734}{27} a^{2} - \frac{791995172}{27} a + \frac{472024472}{27} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{2} + 1\) , \( a^{4} - 4 a^{2} + 1\) , \( a^{4} - 6 a^{2} - 5 a + 3\) , \( -a^{4} - a^{3} + 4 a^{2} + 4 a - 2\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(a^{4}-6a^{2}-5a+3\right){x}-a^{4}-a^{3}+4a^{2}+4a-2$ |
| 16.1-a1 |
16.1-a |
$2$ |
$5$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$33.66304$ |
$(-a^4+a^3+3a^2-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 5 \) |
$1$ |
$1.366182979$ |
0.598158255 |
\( \frac{4298181135954522099}{32} a^{4} - \frac{9202957876278990529}{32} a^{3} - \frac{10989147450090029181}{32} a^{2} + \frac{25434572271835308575}{32} a - \frac{3766605489474797263}{16} \) |
\( \bigl[a^{4} - 5 a^{2} + 4\) , \( -a^{4} + 6 a^{2} - 6\) , \( a^{3} - 2 a - 1\) , \( -583 a^{4} + 549 a^{3} + 2605 a^{2} - 836 a - 2545\) , \( -10426 a^{4} + 9362 a^{3} + 47928 a^{2} - 14450 a - 47312\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+4\right){x}{y}+\left(a^{3}-2a-1\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-6\right){x}^{2}+\left(-583a^{4}+549a^{3}+2605a^{2}-836a-2545\right){x}-10426a^{4}+9362a^{3}+47928a^{2}-14450a-47312$ |
| 16.1-a2 |
16.1-a |
$2$ |
$5$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$33.66304$ |
$(-a^4+a^3+3a^2-a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$4269.321811$ |
0.598158255 |
\( \frac{62067603}{2} a^{4} + \frac{13384031}{2} a^{3} - \frac{294061597}{2} a^{2} - \frac{171274065}{2} a + 51054913 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{4} + 4 a^{2} + 2 a\) , \( a^{4} - 5 a^{2} - a + 3\) , \( -2 a^{4} - a^{3} + 9 a^{2} + 7 a - 3\) , \( a^{4} - 4 a^{3} - a^{2} + 13 a - 4\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+\left(a^{4}-5a^{2}-a+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+2a\right){x}^{2}+\left(-2a^{4}-a^{3}+9a^{2}+7a-3\right){x}+a^{4}-4a^{3}-a^{2}+13a-4$ |
| 16.1-b1 |
16.1-b |
$2$ |
$3$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$33.66304$ |
$(-a^4+a^3+3a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.026204891$ |
$4675.322617$ |
2.14566130 |
\( -\frac{379889489881}{8} a^{4} + \frac{239001814759}{8} a^{3} + \frac{1988084838775}{8} a^{2} - \frac{402357578969}{8} a - \frac{1024333880847}{4} \) |
\( \bigl[a\) , \( -a^{4} + 6 a^{2} - 5\) , \( a^{4} - 5 a^{2} + 3\) , \( -a^{4} + 4 a^{2} - 1\) , \( 3 a^{4} - 4 a^{3} - 13 a^{2} + 9 a + 8\bigr] \) |
${y}^2+a{x}{y}+\left(a^{4}-5a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-5\right){x}^{2}+\left(-a^{4}+4a^{2}-1\right){x}+3a^{4}-4a^{3}-13a^{2}+9a+8$ |
| 16.1-b2 |
16.1-b |
$2$ |
$3$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$33.66304$ |
$(-a^4+a^3+3a^2-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.008734963$ |
$14025.96785$ |
2.14566130 |
\( -\frac{376211473}{2} a^{4} + \frac{1021122263}{2} a^{3} + \frac{131321455}{2} a^{2} - \frac{1354040145}{2} a + 219561705 \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{4} + 6 a^{2} - 5\) , \( 1\) , \( 2 a^{4} + 4 a^{3} - 5 a^{2} - 5 a + 5\) , \( 4 a^{4} + 5 a^{3} - 8 a^{2} - 7 a + 3\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+6a^{2}-5\right){x}^{2}+\left(2a^{4}+4a^{3}-5a^{2}-5a+5\right){x}+4a^{4}+5a^{3}-8a^{2}-7a+3$ |
| 16.1-c1 |
16.1-c |
$2$ |
$2$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{4} \) |
$33.66304$ |
$(-a^4+a^3+3a^2-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$409.2640319$ |
1.43351023 |
\( -94860073825 a^{4} - \frac{40915173965}{2} a^{3} + 449429158962 a^{2} + 261776744552 a - 156059904267 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( a^{2} - a - 1\) , \( a^{2} - 2\) , \( 41 a^{4} + 16 a^{3} - 205 a^{2} - 129 a + 76\) , \( 254 a^{4} + 87 a^{3} - 1250 a^{2} - 773 a + 445\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(41a^{4}+16a^{3}-205a^{2}-129a+76\right){x}+254a^{4}+87a^{3}-1250a^{2}-773a+445$ |
| 16.1-c2 |
16.1-c |
$2$ |
$2$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$33.66304$ |
$(-a^4+a^3+3a^2-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$818.5280639$ |
1.43351023 |
\( \frac{1867107}{2} a^{4} - \frac{5796783}{2} a^{3} + 220121 a^{2} + \frac{16606357}{4} a - \frac{2880145}{2} \) |
\( \bigl[a + 1\) , \( -a^{4} + 4 a^{2} + 2 a - 1\) , \( a^{4} - 5 a^{2} + 4\) , \( a^{3} - a^{2} - 5 a - 3\) , \( 12 a^{4} + 4 a^{3} - 57 a^{2} - 40 a + 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-5a^{2}+4\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+2a-1\right){x}^{2}+\left(a^{3}-a^{2}-5a-3\right){x}+12a^{4}+4a^{3}-57a^{2}-40a+14$ |
| 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 |
\( \frac{264059}{64} a^{4} - \frac{1783929}{64} a^{3} + \frac{447267}{64} a^{2} + \frac{2436259}{64} a - \frac{883495}{64} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 6 a\) , \( a^{2} + a - 2\) , \( -a^{4} + 5 a^{3} - 5 a + 3\) , \( 3 a^{4} - 4 a^{3} - 3 a^{2} + 6 a - 2\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+6a\right){x}^{2}+\left(-a^{4}+5a^{3}-5a+3\right){x}+3a^{4}-4a^{3}-3a^{2}+6a-2$ |
*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.
