| 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 |
| 1.1-a1 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$16201.68209$ |
1.45598 |
\( 1047555090725207805153 a^{5} - 3902722885512039967317 a^{4} - 311029716139316550126 a^{3} + 7558554438729119129733 a^{2} - 2341472887510151657373 a - 1443800639285190993231 \) |
\( \bigl[a\) , \( -a^{5} + 4 a^{4} - 10 a^{2} + 5 a + 4\) , \( 2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 3 a - 4\) , \( 26 a^{5} - 82 a^{4} - 59 a^{3} + 182 a^{2} + 15 a - 83\) , \( -131 a^{5} + 343 a^{4} + 443 a^{3} - 594 a^{2} - 235 a + 205\bigr] \) |
${y}^2+a{x}{y}+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-3a-4\right){y}={x}^{3}+\left(-a^{5}+4a^{4}-10a^{2}+5a+4\right){x}^{2}+\left(26a^{5}-82a^{4}-59a^{3}+182a^{2}+15a-83\right){x}-131a^{5}+343a^{4}+443a^{3}-594a^{2}-235a+205$ |
| 1.1-a2 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$16201.68209$ |
1.45598 |
\( -290305616924071821546 a^{5} + 470800962496801932003 a^{4} + 1519801799571398852784 a^{3} + 62538881102492924502 a^{2} - 784722171334896713385 a - 210632353343743523778 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 3 a - 1\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 8 a^{2} + a - 3\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 2 a^{2} + 6 a + 2\) , \( -14 a^{5} + 50 a^{4} + 10 a^{3} - 101 a^{2} + 23 a + 17\) , \( 178 a^{5} - 666 a^{4} - 37 a^{3} + 1278 a^{2} - 407 a - 247\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+3a-1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+2a^{2}+6a+2\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+8a^{2}+a-3\right){x}^{2}+\left(-14a^{5}+50a^{4}+10a^{3}-101a^{2}+23a+17\right){x}+178a^{5}-666a^{4}-37a^{3}+1278a^{2}-407a-247$ |
| 1.1-a3 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$259226.9134$ |
1.45598 |
\( 18907500780 a^{5} - 70452166815 a^{4} - 5568519933 a^{3} + 136415319255 a^{2} - 42339768615 a - 26009898327 \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a + 2\) , \( a^{4} - 3 a^{3} - 3 a^{2} + 5 a + 2\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a + 1\) , \( -20 a^{5} + 39 a^{4} + 110 a^{3} - 50 a^{2} - 139 a - 49\) , \( -14 a^{5} + 37 a^{4} + 50 a^{3} - 67 a^{2} - 48 a + 6\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a+2\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a+1\right){y}={x}^{3}+\left(a^{4}-3a^{3}-3a^{2}+5a+2\right){x}^{2}+\left(-20a^{5}+39a^{4}+110a^{3}-50a^{2}-139a-49\right){x}-14a^{5}+37a^{4}+50a^{3}-67a^{2}-48a+6$ |
| 1.1-a4 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$259226.9134$ |
1.45598 |
\( -5246709264 a^{5} + 8508915108 a^{4} + 27468776862 a^{3} + 1131975675 a^{2} - 14182156989 a - 3806835696 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 3 a - 1\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 8 a^{2} + a - 3\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 2 a^{2} + 6 a + 2\) , \( -29 a^{5} + 105 a^{4} + 15 a^{3} - 201 a^{2} + 53 a + 37\) , \( 84 a^{5} - 313 a^{4} - 21 a^{3} + 607 a^{2} - 195 a - 118\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+3a-1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+2a^{2}+6a+2\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+8a^{2}+a-3\right){x}^{2}+\left(-29a^{5}+105a^{4}+15a^{3}-201a^{2}+53a+37\right){x}+84a^{5}-313a^{4}-21a^{3}+607a^{2}-195a-118$ |
| 1.1-a5 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$7200.747597$ |
1.45598 |
\( 71082279 a^{5} - 264818403 a^{4} - 21106089 a^{3} + 512883009 a^{2} - 158878584 a - 97968420 \) |
\( \bigl[a\) , \( 2 a^{4} - 5 a^{3} - 6 a^{2} + 5 a + 2\) , \( 0\) , \( -a^{5} + 9 a^{3} + 6 a^{2} - 5 a - 2\) , \( 2 a^{5} - 4 a^{4} - 8 a^{3} + 4 a + 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(2a^{4}-5a^{3}-6a^{2}+5a+2\right){x}^{2}+\left(-a^{5}+9a^{3}+6a^{2}-5a-2\right){x}+2a^{5}-4a^{4}-8a^{3}+4a+1$ |
| 1.1-a6 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$7200.747597$ |
1.45598 |
\( -19765215 a^{5} + 32166153 a^{4} + 103258071 a^{3} + 3738555 a^{2} - 53291520 a - 14082066 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 3 a - 1\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 5 a^{2}\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 3 a^{2} + 4 a + 1\) , \( -a^{5} + 10 a^{3} + 5 a^{2} - 12 a - 6\) , \( -2 a^{5} + 5 a^{4} + 8 a^{3} - 10 a^{2} - 8 a\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+3a-1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+3a^{2}+4a+1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-5a^{2}\right){x}^{2}+\left(-a^{5}+10a^{3}+5a^{2}-12a-6\right){x}-2a^{5}+5a^{4}+8a^{3}-10a^{2}-8a$ |
| 1.1-a7 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$28802.99038$ |
1.45598 |
\( -1223100 a^{5} + 5079429 a^{4} - 2339766 a^{3} - 5159619 a^{2} + 1664388 a + 1391688 \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 3 a\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a + 1\) , \( 3 a^{5} - 9 a^{4} - 7 a^{3} + 16 a^{2} + 2 a - 1\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 4 a^{2} + 19 a + 4\) , \( a^{5} - 11 a^{3} - 3 a^{2} + 16 a + 4\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+3a\right){x}{y}+\left(3a^{5}-9a^{4}-7a^{3}+16a^{2}+2a-1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a+1\right){x}^{2}+\left(2a^{5}-3a^{4}-14a^{3}+4a^{2}+19a+4\right){x}+a^{5}-11a^{3}-3a^{2}+16a+4$ |
| 1.1-a8 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$28802.99038$ |
1.45598 |
\( 2983959 a^{5} - 6655446 a^{4} - 14062491 a^{3} + 10072512 a^{2} + 16683570 a + 3880170 \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 3 a - 1\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 7 a^{2} - a + 3\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 3 a - 1\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 6 a^{2} - a\) , \( a^{2} - 2\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+3a-1\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+3a-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-7a^{2}-a+3\right){x}^{2}+\left(-a^{5}+3a^{4}+3a^{3}-6a^{2}-a\right){x}+a^{2}-2$ |
| 1.1-a9 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$64806.72837$ |
1.45598 |
\( 18813667668606 a^{5} + 3623676360669 a^{4} - 44872022196405 a^{3} - 11563135347816 a^{2} + 19524436288452 a + 5892882391701 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 2 a - 2\) , \( 3 a^{5} - 11 a^{4} - a^{3} + 20 a^{2} - 5 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 5 a^{2} - 1\) , \( 4 a^{5} - 17 a^{4} + 6 a^{3} + 34 a^{2} - 25 a - 8\) , \( 7 a^{5} - 22 a^{4} - 13 a^{3} + 36 a^{2} + 5 a + 4\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+2a-2\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+5a^{2}-1\right){y}={x}^{3}+\left(3a^{5}-11a^{4}-a^{3}+20a^{2}-5a-3\right){x}^{2}+\left(4a^{5}-17a^{4}+6a^{3}+34a^{2}-25a-8\right){x}+7a^{5}-22a^{4}-13a^{3}+36a^{2}+5a+4$ |
| 1.1-a10 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$1800.186899$ |
1.45598 |
\( -15451874918442 a^{5} + 66365894885544 a^{4} - 39676952838168 a^{3} - 56373607858509 a^{2} + 26291672187039 a + 12099308684112 \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 3 a\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a + 1\) , \( 3 a^{5} - 9 a^{4} - 7 a^{3} + 16 a^{2} + 2 a - 1\) , \( 7 a^{5} - 23 a^{4} - 14 a^{3} + 54 a^{2} + 4 a - 26\) , \( 15 a^{5} - 50 a^{4} - 29 a^{3} + 118 a^{2} + 8 a - 55\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+3a\right){x}{y}+\left(3a^{5}-9a^{4}-7a^{3}+16a^{2}+2a-1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a+1\right){x}^{2}+\left(7a^{5}-23a^{4}-14a^{3}+54a^{2}+4a-26\right){x}+15a^{5}-50a^{4}-29a^{3}+118a^{2}+8a-55$ |
| 1.1-a11 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$1800.186899$ |
1.45598 |
\( 43984819519524 a^{5} - 98139433205853 a^{4} - 207397767413889 a^{3} + 148453629100209 a^{2} + 246075398946873 a + 57215861457597 \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 3 a - 1\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 7 a^{2} - a + 3\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 3 a - 1\) , \( -6 a^{5} + 18 a^{4} + 18 a^{3} - 46 a^{2} - 6 a + 15\) , \( -8 a^{5} + 28 a^{4} + 2 a^{3} - 40 a^{2} - a + 11\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+3a-1\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+3a-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-7a^{2}-a+3\right){x}^{2}+\left(-6a^{5}+18a^{4}+18a^{3}-46a^{2}-6a+15\right){x}-8a^{5}+28a^{4}+2a^{3}-40a^{2}-a+11$ |
| 1.1-a12 |
1.1-a |
$12$ |
$24$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$110.48455$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$64806.72837$ |
1.45598 |
\( -1954592591837922 a^{5} + 6476002061311791 a^{4} + 3835341899210817 a^{3} - 14883467264166420 a^{2} - 1201926423969036 a + 6240249347843781 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 2 a - 1\) , \( -a^{5} + 3 a^{4} + a^{3} - 2 a^{2} + a - 3\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 3 a\) , \( -20 a^{5} + 73 a^{4} + 12 a^{3} - 141 a^{2} + 32 a + 27\) , \( 71 a^{5} - 265 a^{4} - 19 a^{3} + 514 a^{2} - 165 a - 101\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+2a-1\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+3a\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+a^{3}-2a^{2}+a-3\right){x}^{2}+\left(-20a^{5}+73a^{4}+12a^{3}-141a^{2}+32a+27\right){x}+71a^{5}-265a^{4}-19a^{3}+514a^{2}-165a-101$ |
| 8.1-a1 |
8.1-a |
$4$ |
$6$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$131.38901$ |
$(2a^5-6a^4-5a^3+12a^2+a-3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.060180713$ |
$112143.1624$ |
2.72921 |
\( -\frac{1960153065}{8} a^{5} + \frac{3668929875}{8} a^{4} + \frac{4656767625}{4} a^{3} - \frac{1846427769}{8} a^{2} - \frac{2346792651}{4} a - \frac{143418177}{4} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 7 a^{3} + 7 a^{2} + 5 a + 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 2 a^{2} + 4 a + 2\) , \( a^{5} - 4 a^{4} + 9 a^{2} - 2 a - 3\) , \( 49 a^{5} - 82 a^{4} - 257 a^{3} + 11 a^{2} + 153 a + 33\) , \( -325 a^{5} + 527 a^{4} + 1699 a^{3} + 73 a^{2} - 864 a - 227\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-7a^{3}+7a^{2}+5a+1\right){x}{y}+\left(a^{5}-4a^{4}+9a^{2}-2a-3\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+2a^{2}+4a+2\right){x}^{2}+\left(49a^{5}-82a^{4}-257a^{3}+11a^{2}+153a+33\right){x}-325a^{5}+527a^{4}+1699a^{3}+73a^{2}-864a-227$ |
| 8.1-a2 |
8.1-a |
$4$ |
$6$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$131.38901$ |
$(2a^5-6a^4-5a^3+12a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.090271069$ |
$12460.35138$ |
2.72921 |
\( \frac{1539}{2} a^{5} + 5994 a^{4} - \frac{32967}{4} a^{3} - \frac{32481}{4} a^{2} + 6318 a + \frac{16713}{4} \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 2 a - 2\) , \( a^{5} - 3 a^{4} - a^{3} + 2 a^{2} - a + 2\) , \( 3 a^{5} - 9 a^{4} - 7 a^{3} + 16 a^{2} + 3 a - 2\) , \( -4 a^{5} + 12 a^{4} + 11 a^{3} - 24 a^{2} - 7 a + 9\) , \( -6 a^{5} + 21 a^{4} + 8 a^{3} - 45 a^{2} + a + 12\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+2a-2\right){x}{y}+\left(3a^{5}-9a^{4}-7a^{3}+16a^{2}+3a-2\right){y}={x}^{3}+\left(a^{5}-3a^{4}-a^{3}+2a^{2}-a+2\right){x}^{2}+\left(-4a^{5}+12a^{4}+11a^{3}-24a^{2}-7a+9\right){x}-6a^{5}+21a^{4}+8a^{3}-45a^{2}+a+12$ |
| 8.1-a3 |
8.1-a |
$4$ |
$6$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{3} \) |
$131.38901$ |
$(2a^5-6a^4-5a^3+12a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$0.180542139$ |
$12460.35138$ |
2.72921 |
\( \frac{1631907}{2} a^{5} - 1901718 a^{4} - 3607578 a^{3} + 2961927 a^{2} + \frac{8281521}{2} a + \frac{1836081}{2} \) |
\( \bigl[a^{4} - 3 a^{3} - 2 a^{2} + 5 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - a - 2\) , \( 3 a^{5} - 9 a^{4} - 7 a^{3} + 16 a^{2} + 2 a - 2\) , \( -6 a^{4} + 14 a^{3} + 23 a^{2} - 16 a - 12\) , \( -5 a^{5} + 14 a^{4} + 14 a^{3} - 23 a^{2} - 6 a + 3\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}-2a^{2}+5a+1\right){x}{y}+\left(3a^{5}-9a^{4}-7a^{3}+16a^{2}+2a-2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-a-2\right){x}^{2}+\left(-6a^{4}+14a^{3}+23a^{2}-16a-12\right){x}-5a^{5}+14a^{4}+14a^{3}-23a^{2}-6a+3$ |
| 8.1-a4 |
8.1-a |
$4$ |
$6$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{18} \) |
$131.38901$ |
$(2a^5-6a^4-5a^3+12a^2+a-3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.030090356$ |
$112143.1624$ |
2.72921 |
\( \frac{39971799}{32} a^{5} - \frac{176125095}{64} a^{4} - \frac{384657849}{64} a^{3} + \frac{134734221}{32} a^{2} + \frac{453505185}{64} a + \frac{52575327}{32} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 5 a^{2} - 1\) , \( 2 a^{5} - 8 a^{4} + a^{3} + 16 a^{2} - 7 a - 6\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 4 a\) , \( 4 a^{5} - 15 a^{4} - a^{3} + 27 a^{2} - 7 a - 3\) , \( 15 a^{5} - 58 a^{4} + a^{3} + 117 a^{2} - 47 a - 26\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+5a^{2}-1\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+4a\right){y}={x}^{3}+\left(2a^{5}-8a^{4}+a^{3}+16a^{2}-7a-6\right){x}^{2}+\left(4a^{5}-15a^{4}-a^{3}+27a^{2}-7a-3\right){x}+15a^{5}-58a^{4}+a^{3}+117a^{2}-47a-26$ |
| 8.2-a1 |
8.2-a |
$4$ |
$6$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{9} \) |
$131.38901$ |
$(-a^5+3a^4+3a^3-6a^2-2a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.060180713$ |
$112143.1624$ |
2.72921 |
\( \frac{6030396549}{8} a^{5} - \frac{5613917409}{2} a^{4} - \frac{1796237775}{8} a^{3} + \frac{43490150775}{8} a^{2} - \frac{6734982483}{4} a - \frac{2076688467}{2} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 12 a^{2} + 2 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 5 a^{2}\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 4 a - 1\) , \( -2 a^{5} + 5 a^{4} + 6 a^{3} - 12 a^{2} - a + 1\) , \( -a^{5} + 4 a^{4} + 3 a^{3} - 5 a^{2} - 5 a - 1\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+12a^{2}+2a-3\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+4a-1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+5a^{2}\right){x}^{2}+\left(-2a^{5}+5a^{4}+6a^{3}-12a^{2}-a+1\right){x}-a^{5}+4a^{4}+3a^{3}-5a^{2}-5a-1$ |
| 8.2-a2 |
8.2-a |
$4$ |
$6$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{3} \) |
$131.38901$ |
$(-a^5+3a^4+3a^3-6a^2-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$0.180542139$ |
$12460.35138$ |
2.72921 |
\( -\frac{560925}{2} a^{5} + \frac{2332395}{2} a^{4} - \frac{1223505}{2} a^{3} - 955395 a^{2} + \frac{828063}{2} a + 192321 \) |
\( \bigl[a^{5} - 4 a^{4} + 9 a^{2} - a - 2\) , \( 2 a^{5} - 7 a^{4} - a^{3} + 11 a^{2} - 3 a\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 3 a^{2} + 3 a + 1\) , \( 2 a^{5} - 10 a^{4} + 6 a^{3} + 23 a^{2} - 12 a - 4\) , \( 2 a^{5} - 7 a^{4} - a^{3} + 11 a^{2} - 4 a - 2\bigr] \) |
${y}^2+\left(a^{5}-4a^{4}+9a^{2}-a-2\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+3a^{2}+3a+1\right){y}={x}^{3}+\left(2a^{5}-7a^{4}-a^{3}+11a^{2}-3a\right){x}^{2}+\left(2a^{5}-10a^{4}+6a^{3}+23a^{2}-12a-4\right){x}+2a^{5}-7a^{4}-a^{3}+11a^{2}-4a-2$ |
| 8.2-a3 |
8.2-a |
$4$ |
$6$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{18} \) |
$131.38901$ |
$(-a^5+3a^4+3a^3-6a^2-2a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.030090356$ |
$112143.1624$ |
2.72921 |
\( -\frac{26156061}{64} a^{5} + \frac{59159331}{32} a^{4} - \frac{5460831}{4} a^{3} - \frac{100068039}{64} a^{2} + \frac{68294601}{64} a + \frac{27853677}{64} \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 3 a^{2} + 4 a + 1\) , \( 3 a^{5} - 10 a^{4} - 4 a^{3} + 18 a^{2} - 2 a - 4\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 12 a^{2} + 2 a - 2\) , \( 8 a^{5} - 30 a^{4} - 5 a^{3} + 68 a^{2} - 11 a - 28\) , \( -17 a^{5} + 50 a^{4} + 47 a^{3} - 103 a^{2} - 22 a + 42\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+3a^{2}+4a+1\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+12a^{2}+2a-2\right){y}={x}^{3}+\left(3a^{5}-10a^{4}-4a^{3}+18a^{2}-2a-4\right){x}^{2}+\left(8a^{5}-30a^{4}-5a^{3}+68a^{2}-11a-28\right){x}-17a^{5}+50a^{4}+47a^{3}-103a^{2}-22a+42$ |
| 8.2-a4 |
8.2-a |
$4$ |
$6$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{6} \) |
$131.38901$ |
$(-a^5+3a^4+3a^3-6a^2-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.090271069$ |
$12460.35138$ |
2.72921 |
\( -\frac{831141}{4} a^{5} + \frac{2766717}{4} a^{4} + 399411 a^{3} - 1594242 a^{2} - \frac{227691}{2} a + \frac{2708343}{4} \) |
\( \bigl[1\) , \( -3 a^{5} + 11 a^{4} + a^{3} - 20 a^{2} + 5 a + 4\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 4 a + 1\) , \( 13 a^{5} - 31 a^{4} - 45 a^{3} + 34 a^{2} + 10 a - 1\) , \( 246 a^{5} - 390 a^{4} - 1309 a^{3} - 84 a^{2} + 685 a + 187\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-3a^{3}-2a^{2}+4a+1\right){y}={x}^{3}+\left(-3a^{5}+11a^{4}+a^{3}-20a^{2}+5a+4\right){x}^{2}+\left(13a^{5}-31a^{4}-45a^{3}+34a^{2}+10a-1\right){x}+246a^{5}-390a^{4}-1309a^{3}-84a^{2}+685a+187$ |
| 19.1-a1 |
19.1-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.171686133$ |
$4391.101830$ |
3.65845 |
\( \frac{23124289257534353484426644431}{19} a^{5} - \frac{86150784525175101958286225743}{19} a^{4} - \frac{6865835671661430076219319769}{19} a^{3} + \frac{166851558204829465678474520559}{19} a^{2} - \frac{51686920159493063147513778549}{19} a - \frac{31871224631278766391580544681}{19} \) |
\( \bigl[2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 3 a - 3\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 7 a^{2} + 4 a + 1\) , \( a^{5} - 4 a^{4} + 9 a^{2} - 2 a - 2\) , \( -28 a^{4} + 66 a^{3} + 94 a^{2} - 49 a - 39\) , \( 85 a^{5} - 106 a^{4} - 526 a^{3} - 98 a^{2} + 262 a + 99\bigr] \) |
${y}^2+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-3a-3\right){x}{y}+\left(a^{5}-4a^{4}+9a^{2}-2a-2\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-7a^{3}+7a^{2}+4a+1\right){x}^{2}+\left(-28a^{4}+66a^{3}+94a^{2}-49a-39\right){x}+85a^{5}-106a^{4}-526a^{3}-98a^{2}+262a+99$ |
| 19.1-a2 |
19.1-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.085843066$ |
$70257.62929$ |
3.65845 |
\( \frac{7367859613548541}{361} a^{5} - \frac{27449357572379474}{361} a^{4} - \frac{2187592472375510}{361} a^{3} + \frac{53162233576529340}{361} a^{2} - \frac{16468483366258594}{361} a - \frac{10154807691749024}{361} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 7 a^{3} + 7 a^{2} + 5 a + 2\) , \( -2 a^{5} + 8 a^{4} - a^{3} - 16 a^{2} + 8 a + 6\) , \( 2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 3 a - 4\) , \( 6 a^{4} - 18 a^{3} - 16 a^{2} + 39 a + 16\) , \( -3 a^{5} - 2 a^{4} + 38 a^{3} + 16 a^{2} - 55 a - 18\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-7a^{3}+7a^{2}+5a+2\right){x}{y}+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-3a-4\right){y}={x}^{3}+\left(-2a^{5}+8a^{4}-a^{3}-16a^{2}+8a+6\right){x}^{2}+\left(6a^{4}-18a^{3}-16a^{2}+39a+16\right){x}-3a^{5}-2a^{4}+38a^{3}+16a^{2}-55a-18$ |
| 19.1-a3 |
19.1-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.042921533$ |
$70257.62929$ |
3.65845 |
\( \frac{462887088132}{130321} a^{5} - \frac{1241367439896}{130321} a^{4} - \frac{394283645968}{130321} a^{3} + \frac{2363655992285}{130321} a^{2} - \frac{630716721470}{130321} a - \frac{408962737675}{130321} \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 2 a^{2} + 6 a + 3\) , \( -3 a^{5} + 10 a^{4} + 4 a^{3} - 18 a^{2} + 3 a + 3\) , \( a + 1\) , \( 8 a^{5} - 28 a^{4} - 15 a^{3} + 53 a^{2} + 8 a - 5\) , \( 4 a^{5} - 25 a^{3} - 3 a^{2} + 32 a + 8\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+2a^{2}+6a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3a^{5}+10a^{4}+4a^{3}-18a^{2}+3a+3\right){x}^{2}+\left(8a^{5}-28a^{4}-15a^{3}+53a^{2}+8a-5\right){x}+4a^{5}-25a^{3}-3a^{2}+32a+8$ |
| 19.1-a4 |
19.1-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{2} \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.085843066$ |
$17564.40732$ |
3.65845 |
\( -\frac{2079370954173}{361} a^{5} + \frac{7872098177879}{361} a^{4} + \frac{1579776327472}{361} a^{3} - \frac{19683993167870}{361} a^{2} + \frac{3244099809177}{361} a + \frac{10719710008682}{361} \) |
\( \bigl[2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 2 a - 4\) , \( -3 a^{5} + 10 a^{4} + 4 a^{3} - 18 a^{2} + a + 2\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 3 a\) , \( 4 a^{5} - 25 a^{4} + 33 a^{3} + 25 a^{2} - 16 a - 6\) , \( -17 a^{5} - 52 a^{4} + 325 a^{3} + 108 a^{2} - 181 a - 57\bigr] \) |
${y}^2+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-2a-4\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+3a\right){y}={x}^{3}+\left(-3a^{5}+10a^{4}+4a^{3}-18a^{2}+a+2\right){x}^{2}+\left(4a^{5}-25a^{4}+33a^{3}+25a^{2}-16a-6\right){x}-17a^{5}-52a^{4}+325a^{3}+108a^{2}-181a-57$ |
| 19.1-a5 |
19.1-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.171686133$ |
$17564.40732$ |
3.65845 |
\( -\frac{27798759514933}{19} a^{5} + \frac{119557629105121}{19} a^{4} - \frac{72127579217974}{19} a^{3} - \frac{100765323762346}{19} a^{2} + \frac{47682008991727}{19} a + \frac{21370025948812}{19} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 4 a^{3} + 9 a^{2} + a\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 2 a - 3\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 2 a - 1\) , \( 5 a^{5} - 2 a^{4} - 39 a^{3} - 26 a^{2} + 23 a + 14\) , \( 42 a^{5} - 70 a^{4} - 216 a^{3} - a^{2} + 111 a + 26\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-4a^{3}+9a^{2}+a\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+2a-1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+2a-3\right){x}^{2}+\left(5a^{5}-2a^{4}-39a^{3}-26a^{2}+23a+14\right){x}+42a^{5}-70a^{4}-216a^{3}-a^{2}+111a+26$ |
| 19.1-a6 |
19.1-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{8} \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.085843066$ |
$4391.101830$ |
3.65845 |
\( \frac{4110731615569027139525896}{16983563041} a^{5} + \frac{791763463112980836224588}{16983563041} a^{4} - \frac{9804405077002193334067110}{16983563041} a^{3} - \frac{2526511571634763795451560}{16983563041} a^{2} + \frac{4266031822728134341447205}{16983563041} a + \frac{1287577482188400249527159}{16983563041} \) |
\( \bigl[2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 2 a - 4\) , \( 2 a^{4} - 5 a^{3} - 7 a^{2} + 6 a + 4\) , \( 3 a^{5} - 10 a^{4} - 4 a^{3} + 18 a^{2} - 2 a - 2\) , \( -19 a^{5} + 71 a^{4} - 15 a^{3} - 60 a^{2} + 7 a - 4\) , \( 125 a^{5} - 203 a^{4} - 928 a^{3} + 686 a^{2} + 890 a - 1\bigr] \) |
${y}^2+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-2a-4\right){x}{y}+\left(3a^{5}-10a^{4}-4a^{3}+18a^{2}-2a-2\right){y}={x}^{3}+\left(2a^{4}-5a^{3}-7a^{2}+6a+4\right){x}^{2}+\left(-19a^{5}+71a^{4}-15a^{3}-60a^{2}+7a-4\right){x}+125a^{5}-203a^{4}-928a^{3}+686a^{2}+890a-1$ |
| 19.1-b1 |
19.1-b |
$1$ |
$1$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.011581418$ |
$22090.01570$ |
2.48299 |
\( \frac{4632572}{361} a^{5} - \frac{9034681}{361} a^{4} - \frac{21134032}{361} a^{3} + \frac{5640222}{361} a^{2} + \frac{10080580}{361} a + \frac{265883}{361} \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 3 a^{2} + 4 a + 1\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 1\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 7 a^{2} + 4 a + 2\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 7 a^{2} + 3 a\) , \( a^{4} - 2 a^{3} - 4 a^{2} + a\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+3a^{2}+4a+1\right){x}{y}+\left(2a^{5}-5a^{4}-7a^{3}+7a^{2}+4a+2\right){y}={x}^{3}+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+2a-1\right){x}^{2}+\left(2a^{5}-5a^{4}-7a^{3}+7a^{2}+3a\right){x}+a^{4}-2a^{3}-4a^{2}+a$ |
| 19.1-c1 |
19.1-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{8} \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$832.2288758$ |
1.34620 |
\( -\frac{13056686695417328530282}{16983563041} a^{5} + \frac{21174809386023941145268}{16983563041} a^{4} + \frac{68353652995293104125553}{16983563041} a^{3} + \frac{2811683209541884544623}{16983563041} a^{2} - \frac{35293120083812478704619}{16983563041} a - \frac{9472806085455846272038}{16983563041} \) |
\( \bigl[a\) , \( -a^{5} + 4 a^{4} - a^{3} - 6 a^{2} + 2 a\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a + 2\) , \( 3 a^{5} - 11 a^{4} - 3 a^{3} + 31 a^{2} - 7 a - 17\) , \( -55 a^{5} + 129 a^{4} + 242 a^{3} - 218 a^{2} - 272 a - 37\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a+2\right){y}={x}^{3}+\left(-a^{5}+4a^{4}-a^{3}-6a^{2}+2a\right){x}^{2}+\left(3a^{5}-11a^{4}-3a^{3}+31a^{2}-7a-17\right){x}-55a^{5}+129a^{4}+242a^{3}-218a^{2}-272a-37$ |
| 19.1-c2 |
19.1-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$13315.66201$ |
1.34620 |
\( -\frac{33505029683}{130321} a^{5} + \frac{54147061434}{130321} a^{4} + \frac{173517900907}{130321} a^{3} + \frac{12477596534}{130321} a^{2} - \frac{82655635841}{130321} a - \frac{21710142011}{130321} \) |
\( \bigl[a\) , \( -a^{5} + 4 a^{4} - a^{3} - 6 a^{2} + 2 a\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a + 2\) , \( -7 a^{5} + 14 a^{4} + 37 a^{3} - 19 a^{2} - 47 a - 12\) , \( -16 a^{5} + 35 a^{4} + 78 a^{3} - 56 a^{2} - 90 a - 21\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a+2\right){y}={x}^{3}+\left(-a^{5}+4a^{4}-a^{3}-6a^{2}+2a\right){x}^{2}+\left(-7a^{5}+14a^{4}+37a^{3}-19a^{2}-47a-12\right){x}-16a^{5}+35a^{4}+78a^{3}-56a^{2}-90a-21$ |
| 19.1-c3 |
19.1-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$13315.66201$ |
1.34620 |
\( -\frac{33247745917}{361} a^{5} + \frac{143126093219}{361} a^{4} - \frac{86935682991}{361} a^{3} - \frac{119683012699}{361} a^{2} + \frac{56903545723}{361} a + \frac{25420628753}{361} \) |
\( \bigl[2 a^{5} - 7 a^{4} - 2 a^{3} + 13 a^{2} - 2\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 6 a^{2} + 5 a - 1\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 2 a - 1\) , \( -9 a^{5} + 21 a^{4} + 39 a^{3} - 31 a^{2} - 44 a - 10\) , \( -9 a^{5} + 20 a^{4} + 43 a^{3} - 31 a^{2} - 51 a - 12\bigr] \) |
${y}^2+\left(2a^{5}-7a^{4}-2a^{3}+13a^{2}-2\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+2a-1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+6a^{2}+5a-1\right){x}^{2}+\left(-9a^{5}+21a^{4}+39a^{3}-31a^{2}-44a-10\right){x}-9a^{5}+20a^{4}+43a^{3}-31a^{2}-51a-12$ |
| 19.1-c4 |
19.1-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6657.831007$ |
1.34620 |
\( -\frac{951135646}{19} a^{5} + \frac{3381018554}{19} a^{4} + \frac{1839053910}{19} a^{3} - \frac{7781701150}{19} a^{2} - \frac{557378211}{19} a + \frac{3266300159}{19} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 2 a^{2} + 6 a + 3\) , \( 43 a^{5} - 96 a^{4} - 204 a^{3} + 147 a^{2} + 243 a + 56\) , \( 142 a^{5} - 317 a^{4} - 669 a^{3} + 480 a^{2} + 794 a + 184\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+2a^{2}+6a+3\right){y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(43a^{5}-96a^{4}-204a^{3}+147a^{2}+243a+56\right){x}+142a^{5}-317a^{4}-669a^{3}+480a^{2}+794a+184$ |
| 19.1-c5 |
19.1-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{2} \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3328.915503$ |
1.34620 |
\( \frac{498676898508}{361} a^{5} - \frac{1112663567594}{361} a^{4} - \frac{2351377386722}{361} a^{3} + \frac{1683106178272}{361} a^{2} + \frac{2789893039153}{361} a + \frac{648687746667}{361} \) |
\( \bigl[a^{4} - 3 a^{3} - 2 a^{2} + 4 a + 1\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 2 a\) , \( 2 a^{5} - 6 a^{4} - 4 a^{3} + 9 a^{2} + a\) , \( 2 a^{5} - 7 a^{4} - a^{3} + 12 a^{2} - 7 a + 1\) , \( -4 a^{5} + 11 a^{4} + 14 a^{3} - 23 a^{2} - 15 a + 4\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}-2a^{2}+4a+1\right){x}{y}+\left(2a^{5}-6a^{4}-4a^{3}+9a^{2}+a\right){y}={x}^{3}+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+2a\right){x}^{2}+\left(2a^{5}-7a^{4}-a^{3}+12a^{2}-7a+1\right){x}-4a^{5}+11a^{4}+14a^{3}-23a^{2}-15a+4$ |
| 19.1-c6 |
19.1-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$141.20964$ |
$(-2a^5+7a^4+2a^3-13a^2+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$416.1144379$ |
1.34620 |
\( -\frac{2313213743455271842}{19} a^{5} + \frac{9948750803795636806}{19} a^{4} - \frac{6002035047527090789}{19} a^{3} - \frac{8384877296682787476}{19} a^{2} + \frac{3967749441287619592}{19} a + \frac{1778246611324120358}{19} \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 3 a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - a - 4\) , \( 2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 3 a - 3\) , \( -16 a^{5} + 32 a^{4} + 73 a^{3} - 25 a^{2} - 42 a - 2\) , \( 9 a^{5} - 28 a^{4} - 24 a^{3} + 68 a^{2} + 23 a - 25\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+3a-2\right){x}{y}+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-a-4\right){x}^{2}+\left(-16a^{5}+32a^{4}+73a^{3}-25a^{2}-42a-2\right){x}+9a^{5}-28a^{4}-24a^{3}+68a^{2}+23a-25$ |
| 19.2-a1 |
19.2-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$141.20964$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.171686133$ |
$4391.101830$ |
3.65845 |
\( -\frac{6408360887732837596158565972}{19} a^{5} + \frac{10392711337247897147070038630}{19} a^{4} + \frac{33548914797824853850650939600}{19} a^{3} + \frac{1380516540826459832225932126}{19} a^{2} - \frac{17322375414994533661597871477}{19} a - \frac{4649610818191456593315167198}{19} \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 7 a^{2} + 3 a - 2\) , \( -2 a^{5} + 8 a^{4} - a^{3} - 15 a^{2} + 4 a + 4\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 5 a + 1\) , \( -47 a^{5} + 99 a^{4} + 234 a^{3} - 155 a^{2} - 276 a - 60\) , \( 390 a^{5} - 866 a^{4} - 1796 a^{3} + 1260 a^{2} + 2154 a + 525\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+7a^{2}+3a-2\right){x}{y}+\left(a^{4}-3a^{3}-2a^{2}+5a+1\right){y}={x}^{3}+\left(-2a^{5}+8a^{4}-a^{3}-15a^{2}+4a+4\right){x}^{2}+\left(-47a^{5}+99a^{4}+234a^{3}-155a^{2}-276a-60\right){x}+390a^{5}-866a^{4}-1796a^{3}+1260a^{2}+2154a+525$ |
| 19.2-a2 |
19.2-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$141.20964$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.085843066$ |
$70257.62929$ |
3.65845 |
\( -\frac{2041831251519460}{361} a^{5} + \frac{3311324360252060}{361} a^{4} + \frac{10689351764408780}{361} a^{3} + \frac{439861209754569}{361} a^{2} - \frac{5519252413843928}{361} a - \frac{1481458295742348}{361} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 4 a^{3} + 9 a^{2} + a + 1\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 2 a^{2} - 4 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + a + 2\) , \( 8 a^{5} - 29 a^{4} - 6 a^{3} + 63 a^{2} - 5 a - 34\) , \( -22 a^{5} + 75 a^{4} + 38 a^{3} - 170 a^{2} - 7 a + 72\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-4a^{3}+9a^{2}+a+1\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+a+2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-2a^{2}-4a-3\right){x}^{2}+\left(8a^{5}-29a^{4}-6a^{3}+63a^{2}-5a-34\right){x}-22a^{5}+75a^{4}+38a^{3}-170a^{2}-7a+72$ |
| 19.2-a3 |
19.2-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{4} \) |
$141.20964$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.042921533$ |
$70257.62929$ |
3.65845 |
\( -\frac{12880657892353}{130321} a^{5} + \frac{42516078801704}{130321} a^{4} + \frac{25583399211196}{130321} a^{3} - \frac{97330849520122}{130321} a^{2} - \frac{8119229090392}{130321} a + \frac{40748292460719}{130321} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 11 a^{2} + 3 a\) , \( a^{4} - 3 a^{3} - 3 a^{2} + 7 a + 3\) , \( 2 a^{5} - 6 a^{4} - 5 a^{3} + 12 a^{2} + a - 3\) , \( -8 a^{5} + 59 a^{4} - 78 a^{3} - 138 a^{2} + 135 a + 38\) , \( 72 a^{5} - 287 a^{4} + 17 a^{3} + 589 a^{2} - 167 a - 88\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+11a^{2}+3a\right){x}{y}+\left(2a^{5}-6a^{4}-5a^{3}+12a^{2}+a-3\right){y}={x}^{3}+\left(a^{4}-3a^{3}-3a^{2}+7a+3\right){x}^{2}+\left(-8a^{5}+59a^{4}-78a^{3}-138a^{2}+135a+38\right){x}+72a^{5}-287a^{4}+17a^{3}+589a^{2}-167a-88$ |
| 19.2-a4 |
19.2-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{2} \) |
$141.20964$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.085843066$ |
$17564.40732$ |
3.65845 |
\( -\frac{288426768835}{361} a^{5} + \frac{1369697997025}{361} a^{4} - \frac{891592176088}{361} a^{3} - \frac{1167396904946}{361} a^{2} + \frac{573916768327}{361} a + \frac{252838700917}{361} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 12 a^{2} + 2 a - 2\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + a + 1\) , \( 2 a^{5} - 6 a^{4} - 4 a^{3} + 9 a^{2} + a + 1\) , \( -9 a^{5} + 3 a^{4} + 93 a^{3} + 13 a^{2} - 141 a - 42\) , \( 65 a^{5} - 406 a^{4} + 465 a^{3} + 890 a^{2} - 1004 a - 384\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+12a^{2}+2a-2\right){x}{y}+\left(2a^{5}-6a^{4}-4a^{3}+9a^{2}+a+1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+a+1\right){x}^{2}+\left(-9a^{5}+3a^{4}+93a^{3}+13a^{2}-141a-42\right){x}+65a^{5}-406a^{4}+465a^{3}+890a^{2}-1004a-384$ |
| 19.2-a5 |
19.2-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$141.20964$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.171686133$ |
$17564.40732$ |
3.65845 |
\( \frac{79598705797959}{19} a^{5} - \frac{177605491116147}{19} a^{4} - \frac{375328190145260}{19} a^{3} + \frac{268660994067424}{19} a^{2} + \frac{445325790926533}{19} a + \frac{103544099735009}{19} \) |
\( \bigl[2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 2 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a\) , \( 2 a^{5} - 6 a^{4} - 4 a^{3} + 9 a^{2} + 1\) , \( -a^{3} + 9 a^{2} - 2 a - 11\) , \( 4 a^{5} - 11 a^{4} - 10 a^{3} + 22 a^{2} + 8 a - 11\bigr] \) |
${y}^2+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-2a-3\right){x}{y}+\left(2a^{5}-6a^{4}-4a^{3}+9a^{2}+1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a\right){x}^{2}+\left(-a^{3}+9a^{2}-2a-11\right){x}+4a^{5}-11a^{4}-10a^{3}+22a^{2}+8a-11$ |
| 19.2-a6 |
19.2-a |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{8} \) |
$141.20964$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.085843066$ |
$4391.101830$ |
3.65845 |
\( -\frac{427072831343788214303084445}{16983563041} a^{5} + \frac{1414987730177702100448279549}{16983563041} a^{4} + \frac{838011120893187195443257287}{16983563041} a^{3} - \frac{3251994575438214585937115263}{16983563041} a^{2} - \frac{262617453454536429493250343}{16983563041} a + \frac{1363476446975656786487608154}{16983563041} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 12 a^{2} + 2 a - 2\) , \( -3 a^{5} + 11 a^{4} + a^{3} - 20 a^{2} + 6 a + 3\) , \( 2 a^{5} - 6 a^{4} - 4 a^{3} + 9 a^{2}\) , \( 45 a^{5} - 110 a^{4} - 183 a^{3} + 171 a^{2} + 207 a + 39\) , \( 150 a^{5} - 234 a^{4} - 1063 a^{3} + 468 a^{2} + 1216 a + 310\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+12a^{2}+2a-2\right){x}{y}+\left(2a^{5}-6a^{4}-4a^{3}+9a^{2}\right){y}={x}^{3}+\left(-3a^{5}+11a^{4}+a^{3}-20a^{2}+6a+3\right){x}^{2}+\left(45a^{5}-110a^{4}-183a^{3}+171a^{2}+207a+39\right){x}+150a^{5}-234a^{4}-1063a^{3}+468a^{2}+1216a+310$ |
| 19.2-b1 |
19.2-b |
$1$ |
$1$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$141.20964$ |
$(a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.011581418$ |
$22090.01570$ |
2.48299 |
\( -\frac{13779056}{361} a^{5} + \frac{51196858}{361} a^{4} + \frac{4405309}{361} a^{3} - \frac{99111060}{361} a^{2} + \frac{30517352}{361} a + \frac{19021209}{361} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 5 a^{2} - 1\) , \( -a^{5} + 4 a^{4} - a^{3} - 7 a^{2} + 6 a + 1\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 4 a + 2\) , \( 2 a^{5} - 8 a^{4} + a^{3} + 16 a^{2} - 5 a - 1\) , \( -2 a^{5} + 6 a^{4} + 5 a^{3} - 11 a^{2} - a + 1\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+5a^{2}-1\right){x}{y}+\left(a^{4}-3a^{3}-2a^{2}+4a+2\right){y}={x}^{3}+\left(-a^{5}+4a^{4}-a^{3}-7a^{2}+6a+1\right){x}^{2}+\left(2a^{5}-8a^{4}+a^{3}+16a^{2}-5a-1\right){x}-2a^{5}+6a^{4}+5a^{3}-11a^{2}-a+1$ |
| 19.2-c1 |
19.2-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{8} \) |
$141.20964$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$832.2288758$ |
1.34620 |
\( \frac{47114001465343206859462}{16983563041} a^{5} - \frac{175525743994179614064604}{16983563041} a^{4} - \frac{13988626409936625317705}{16983563041} a^{3} + \frac{339947500776695339623229}{16983563041} a^{2} - \frac{105308211569847916364205}{16983563041} a - \frac{64935222920002195949001}{16983563041} \) |
\( \bigl[2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 3 a - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 2 a + 2\) , \( 2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 3 a - 4\) , \( 6 a^{5} - 4 a^{4} - 44 a^{3} - 24 a^{2} + 28 a + 13\) , \( -67 a^{5} + 118 a^{4} + 331 a^{3} - 26 a^{2} - 158 a - 38\bigr] \) |
${y}^2+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-3a-4\right){x}{y}+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-3a-4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+2a+2\right){x}^{2}+\left(6a^{5}-4a^{4}-44a^{3}-24a^{2}+28a+13\right){x}-67a^{5}+118a^{4}+331a^{3}-26a^{2}-158a-38$ |
| 19.2-c2 |
19.2-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{4} \) |
$141.20964$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$13315.66201$ |
1.34620 |
\( \frac{127053440921}{130321} a^{5} - \frac{471555414254}{130321} a^{4} - \frac{43873777303}{130321} a^{3} + \frac{915887520344}{130321} a^{2} - \frac{277300018107}{130321} a - \frac{172757848542}{130321} \) |
\( \bigl[2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 3 a - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 2 a + 2\) , \( 2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 3 a - 4\) , \( a^{5} - 4 a^{4} + a^{3} + 6 a^{2} - 2 a - 2\) , \( -2 a^{4} + 5 a^{3} + 6 a^{2} - 4 a - 3\bigr] \) |
${y}^2+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-3a-4\right){x}{y}+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-3a-4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+2a+2\right){x}^{2}+\left(a^{5}-4a^{4}+a^{3}+6a^{2}-2a-2\right){x}-2a^{4}+5a^{3}+6a^{2}-4a-3$ |
| 19.2-c3 |
19.2-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$141.20964$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$13315.66201$ |
1.34620 |
\( \frac{95798131486}{361} a^{5} - \frac{213785682348}{361} a^{4} - \frac{451690176450}{361} a^{3} + \frac{323552576526}{361} a^{2} + \frac{536163495727}{361} a + \frac{124673046836}{361} \) |
\( \bigl[a + 1\) , \( 3 a^{5} - 11 a^{4} - a^{3} + 20 a^{2} - 5 a - 5\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a + 2\) , \( -4 a^{5} + 16 a^{4} - 4 a^{3} - 24 a^{2} + 14 a - 3\) , \( -37 a^{5} + 134 a^{4} + 25 a^{3} - 267 a^{2} + 60 a + 59\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a+2\right){y}={x}^{3}+\left(3a^{5}-11a^{4}-a^{3}+20a^{2}-5a-5\right){x}^{2}+\left(-4a^{5}+16a^{4}-4a^{3}-24a^{2}+14a-3\right){x}-37a^{5}+134a^{4}+25a^{3}-267a^{2}+60a+59$ |
| 19.2-c4 |
19.2-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{2} \) |
$141.20964$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3328.915503$ |
1.34620 |
\( -\frac{174756576741}{361} a^{5} + \frac{751003080505}{361} a^{4} - \frac{450685013215}{361} a^{3} - \frac{635864882327}{361} a^{2} + \frac{298349517229}{361} a + \frac{135803991326}{361} \) |
\( \bigl[a^{4} - 3 a^{3} - 2 a^{2} + 4 a + 1\) , \( -2 a^{5} + 6 a^{4} + 5 a^{3} - 11 a^{2} - 2 a + 2\) , \( 2 a^{5} - 6 a^{4} - 4 a^{3} + 9 a^{2} + a + 1\) , \( a^{5} - 5 a^{4} + 4 a^{3} + 10 a^{2} - 7 a - 4\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 6 a^{2} - 2\bigr] \) |
${y}^2+\left(a^{4}-3a^{3}-2a^{2}+4a+1\right){x}{y}+\left(2a^{5}-6a^{4}-4a^{3}+9a^{2}+a+1\right){y}={x}^{3}+\left(-2a^{5}+6a^{4}+5a^{3}-11a^{2}-2a+2\right){x}^{2}+\left(a^{5}-5a^{4}+4a^{3}+10a^{2}-7a-4\right){x}-a^{5}+3a^{4}+3a^{3}-6a^{2}-2$ |
| 19.2-c5 |
19.2-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$141.20964$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6657.831007$ |
1.34620 |
\( -\frac{6801778915}{19} a^{5} + \frac{22569865425}{19} a^{4} + \frac{13343268885}{19} a^{3} - \frac{51872981369}{19} a^{2} - \frac{4179889727}{19} a + \frac{21749608418}{19} \) |
\( \bigl[2 a^{5} - 6 a^{4} - 5 a^{3} + 12 a^{2} + 2 a - 2\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 7 a^{2} + 5 a + 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 2 a^{2} + 6 a + 2\) , \( 29 a^{5} - 93 a^{4} - 64 a^{3} + 210 a^{2} + 28 a - 80\) , \( -66 a^{5} + 222 a^{4} + 122 a^{3} - 514 a^{2} - 30 a + 221\bigr] \) |
${y}^2+\left(2a^{5}-6a^{4}-5a^{3}+12a^{2}+2a-2\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+2a^{2}+6a+2\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-7a^{3}+7a^{2}+5a+2\right){x}^{2}+\left(29a^{5}-93a^{4}-64a^{3}+210a^{2}+28a-80\right){x}-66a^{5}+222a^{4}+122a^{3}-514a^{2}-30a+221$ |
| 19.2-c6 |
19.2-c |
$6$ |
$8$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$141.20964$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$416.1144379$ |
1.34620 |
\( \frac{6623704150215885768}{19} a^{5} - \frac{14779207495664405471}{19} a^{4} - \frac{31232479757993970328}{19} a^{3} + \frac{22356281087180938732}{19} a^{2} + \frac{37057289485885900712}{19} a + \frac{8616311978195036512}{19} \) |
\( \bigl[a + 1\) , \( 3 a^{5} - 11 a^{4} - a^{3} + 20 a^{2} - 5 a - 5\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a + 2\) , \( 36 a^{5} - 134 a^{4} - 9 a^{3} + 256 a^{2} - 86 a - 48\) , \( -38 a^{5} + 137 a^{4} + 30 a^{3} - 276 a^{2} + 42 a + 75\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a+2\right){y}={x}^{3}+\left(3a^{5}-11a^{4}-a^{3}+20a^{2}-5a-5\right){x}^{2}+\left(36a^{5}-134a^{4}-9a^{3}+256a^{2}-86a-48\right){x}-38a^{5}+137a^{4}+30a^{3}-276a^{2}+42a+75$ |
| 37.1-a1 |
37.1-a |
$2$ |
$2$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( - 37^{6} \) |
$149.27429$ |
$(2a^5-6a^4-5a^3+11a^2+3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4359.190796$ |
1.76284 |
\( -\frac{12361183028886}{2565726409} a^{5} + \frac{149081813963415}{2565726409} a^{4} - \frac{365347603330524}{2565726409} a^{3} + \frac{151246218863499}{2565726409} a^{2} + \frac{5398766631404}{69343957} a - \frac{118580064059319}{2565726409} \) |
\( \bigl[2 a^{5} - 5 a^{4} - 7 a^{3} + 7 a^{2} + 5 a + 2\) , \( 3 a^{5} - 11 a^{4} - a^{3} + 20 a^{2} - 5 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a + 2\) , \( 11 a^{5} - 37 a^{4} - 15 a^{3} + 71 a^{2} + 2 a - 10\) , \( -11 a^{5} + 50 a^{4} - 23 a^{3} - 95 a^{2} + 63 a + 28\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-7a^{3}+7a^{2}+5a+2\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a+2\right){y}={x}^{3}+\left(3a^{5}-11a^{4}-a^{3}+20a^{2}-5a-3\right){x}^{2}+\left(11a^{5}-37a^{4}-15a^{3}+71a^{2}+2a-10\right){x}-11a^{5}+50a^{4}-23a^{3}-95a^{2}+63a+28$ |
| 37.1-a2 |
37.1-a |
$2$ |
$2$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( - 37^{3} \) |
$149.27429$ |
$(2a^5-6a^4-5a^3+11a^2+3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8718.381593$ |
1.76284 |
\( -\frac{72258285350705}{50653} a^{5} + \frac{237632697402651}{50653} a^{4} + \frac{145229216130753}{50653} a^{3} - \frac{542022303374099}{50653} a^{2} - \frac{1260671253768}{1369} a + \frac{226606377224247}{50653} \) |
\( \bigl[a^{5} - 4 a^{4} + 9 a^{2} - 2 a - 2\) , \( -2 a^{5} + 8 a^{4} - a^{3} - 16 a^{2} + 8 a + 5\) , \( 3 a^{5} - 10 a^{4} - 4 a^{3} + 18 a^{2} - a - 3\) , \( -256 a^{5} + 954 a^{4} + 73 a^{3} - 1843 a^{2} + 580 a + 349\) , \( -2361 a^{5} + 8795 a^{4} + 704 a^{3} - 17035 a^{2} + 5273 a + 3256\bigr] \) |
${y}^2+\left(a^{5}-4a^{4}+9a^{2}-2a-2\right){x}{y}+\left(3a^{5}-10a^{4}-4a^{3}+18a^{2}-a-3\right){y}={x}^{3}+\left(-2a^{5}+8a^{4}-a^{3}-16a^{2}+8a+5\right){x}^{2}+\left(-256a^{5}+954a^{4}+73a^{3}-1843a^{2}+580a+349\right){x}-2361a^{5}+8795a^{4}+704a^{3}-17035a^{2}+5273a+3256$ |
| 37.1-b1 |
37.1-b |
$4$ |
$4$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( -37 \) |
$149.27429$ |
$(2a^5-6a^4-5a^3+11a^2+3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.041603315$ |
$64167.53653$ |
3.23871 |
\( \frac{221293245}{37} a^{5} - \frac{798786946}{37} a^{4} - \frac{195637836}{37} a^{3} + \frac{1762126429}{37} a^{2} - 14209440 a - \frac{328620552}{37} \) |
\( \bigl[2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 3 a - 4\) , \( -a^{5} + 4 a^{4} - a^{3} - 6 a^{2} + 3 a\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 7 a^{2} + 5 a + 2\) , \( 15 a^{5} - 15 a^{4} - 101 a^{3} - 35 a^{2} + 64 a + 21\) , \( 31 a^{5} - 52 a^{4} - 157 a^{3} - 3 a^{2} + 73 a + 19\bigr] \) |
${y}^2+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-3a-4\right){x}{y}+\left(2a^{5}-5a^{4}-7a^{3}+7a^{2}+5a+2\right){y}={x}^{3}+\left(-a^{5}+4a^{4}-a^{3}-6a^{2}+3a\right){x}^{2}+\left(15a^{5}-15a^{4}-101a^{3}-35a^{2}+64a+21\right){x}+31a^{5}-52a^{4}-157a^{3}-3a^{2}+73a+19$ |
| 37.1-b2 |
37.1-b |
$4$ |
$4$ |
6.6.1528713.1 |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37^{4} \) |
$149.27429$ |
$(2a^5-6a^4-5a^3+11a^2+3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.041603315$ |
$16041.88413$ |
3.23871 |
\( \frac{6692477642}{1874161} a^{5} - \frac{25220030133}{1874161} a^{4} - \frac{283402338}{1874161} a^{3} + \frac{47671710014}{1874161} a^{2} - \frac{493103291}{50653} a - \frac{6968853627}{1874161} \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 4 a^{2} + 2 a + 2\) , \( 2 a^{5} - 7 a^{4} - 2 a^{3} + 14 a^{2} - 2 a - 3\) , \( 0\) , \( 6 a^{5} - 16 a^{4} - 17 a^{3} + 22 a^{2} + 7 a + 3\) , \( -31 a^{5} + 45 a^{4} + 174 a^{3} + 28 a^{2} - 91 a - 27\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+4a^{2}+2a+2\right){x}{y}={x}^{3}+\left(2a^{5}-7a^{4}-2a^{3}+14a^{2}-2a-3\right){x}^{2}+\left(6a^{5}-16a^{4}-17a^{3}+22a^{2}+7a+3\right){x}-31a^{5}+45a^{4}+174a^{3}+28a^{2}-91a-27$ |
*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.
