| 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 |
$8$ |
$12$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$4553.484644$ |
1.26451 |
\( 22392918326848 a^{5} - 49652046420192 a^{4} - 83647986205696 a^{3} + 136065840190624 a^{2} + 106497343113920 a - 28610208943792 \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} + a - 2\) , \( -a^{5} + 3 a^{4} + 4 a^{3} - 11 a^{2} - 7 a + 4\) , \( a^{2} - a\) , \( -a^{5} - a^{4} + 6 a^{3} + 6 a^{2} - 1\) , \( -a^{5} + a^{4} + 4 a^{3} - a - 3\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+9a^{2}+a-2\right){x}{y}+\left(a^{2}-a\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+4a^{3}-11a^{2}-7a+4\right){x}^{2}+\left(-a^{5}-a^{4}+6a^{3}+6a^{2}-1\right){x}-a^{5}+a^{4}+4a^{3}-a-3$ |
| 1.1-a2 |
1.1-a |
$8$ |
$12$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$4553.484644$ |
1.26451 |
\( -3399070310880 a^{5} + 15063420699136 a^{4} - 14767100645984 a^{3} - 9450606119232 a^{2} + 13529761466464 a - 2374262400912 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 7 a^{3} + 16 a^{2} + 7 a - 5\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 9 a^{2} + 10 a - 6\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a\) , \( 10 a^{5} - 19 a^{4} - 44 a^{3} + 60 a^{2} + 53 a - 14\) , \( 13 a^{5} - 23 a^{4} - 59 a^{3} + 71 a^{2} + 74 a - 18\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-7a^{3}+16a^{2}+7a-5\right){x}{y}+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-6a^{3}+9a^{2}+10a-6\right){x}^{2}+\left(10a^{5}-19a^{4}-44a^{3}+60a^{2}+53a-14\right){x}+13a^{5}-23a^{4}-59a^{3}+71a^{2}+74a-18$ |
| 1.1-a3 |
1.1-a |
$8$ |
$12$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$4553.484644$ |
1.26451 |
\( 3399070310880 a^{5} - 1931930855264 a^{4} - 11495879041760 a^{3} + 2637913028832 a^{2} + 6414421467808 a - 1397857311408 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 13 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + a^{3} - 6 a^{2} + a\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + 2 a - 2\) , \( -2 a^{5} + 7 a^{4} - 3 a^{3} - 5 a^{2} + a - 3\) , \( -3 a^{5} + 14 a^{4} - 15 a^{3} - 8 a^{2} + 14 a - 5\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+13a^{2}+2a-2\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+2a-2\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+a^{3}-6a^{2}+a\right){x}^{2}+\left(-2a^{5}+7a^{4}-3a^{3}-5a^{2}+a-3\right){x}-3a^{5}+14a^{4}-15a^{3}-8a^{2}+14a-5$ |
| 1.1-a4 |
1.1-a |
$8$ |
$12$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$18213.93857$ |
1.26451 |
\( 3047424 a^{5} - 7618560 a^{4} - 9142272 a^{3} + 21331968 a^{2} + 6094848 a - 2220032 \) |
\( \bigl[0\) , \( -2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 7 a + 4\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 13 a^{2} + 2 a - 3\) , \( 3 a^{5} - 8 a^{4} - 6 a^{3} + 15 a^{2} + 9 a - 2\) , \( -4 a^{4} + 15 a^{3} - 8 a^{2} - 13 a + 2\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+13a^{2}+2a-3\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+6a^{3}-13a^{2}-7a+4\right){x}^{2}+\left(3a^{5}-8a^{4}-6a^{3}+15a^{2}+9a-2\right){x}-4a^{4}+15a^{3}-8a^{2}-13a+2$ |
| 1.1-a5 |
1.1-a |
$8$ |
$12$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$18213.93857$ |
1.26451 |
\( -3047424 a^{5} + 7618560 a^{4} + 9142272 a^{3} - 21331968 a^{2} - 6094848 a + 11493376 \) |
\( \bigl[0\) , \( a^{4} - a^{3} - 4 a^{2} + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a\) , \( 3 a^{5} - 10 a^{4} - 7 a^{3} + 34 a^{2} + 6 a - 21\) , \( 14 a^{5} - 39 a^{4} - 37 a^{3} + 118 a^{2} + 26 a - 66\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3\right){x}^{2}+\left(3a^{5}-10a^{4}-7a^{3}+34a^{2}+6a-21\right){x}+14a^{5}-39a^{4}-37a^{3}+118a^{2}+26a-66$ |
| 1.1-a6 |
1.1-a |
$8$ |
$12$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$4553.484644$ |
1.26451 |
\( -9261428482976 a^{5} + 10257576888576 a^{4} + 37934719920608 a^{3} - 11563634842304 a^{2} - 21883503634144 a + 4893906297200 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 4 a - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 2\) , \( 7 a^{5} - 16 a^{4} - 27 a^{3} + 46 a^{2} + 35 a - 10\) , \( 20 a^{5} - 45 a^{4} - 74 a^{3} + 123 a^{2} + 95 a - 26\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+4a-4\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+3a-1\right){x}^{2}+\left(7a^{5}-16a^{4}-27a^{3}+46a^{2}+35a-10\right){x}+20a^{5}-45a^{4}-74a^{3}+123a^{2}+95a-26$ |
| 1.1-a7 |
1.1-a |
$8$ |
$12$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$4553.484644$ |
1.26451 |
\( 9261428482976 a^{5} - 36049565526304 a^{4} + 13649257354848 a^{3} + 71171701421216 a^{2} - 63516551582496 a + 10377636146960 \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a - 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 4 a + 3\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 13 a^{2} + 2 a - 3\) , \( -8 a^{5} + 22 a^{4} + 20 a^{3} - 65 a^{2} - 13 a + 32\) , \( -14 a^{5} + 39 a^{4} + 35 a^{3} - 116 a^{2} - 22 a + 59\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+2a-1\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+13a^{2}+2a-3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-4a+3\right){x}^{2}+\left(-8a^{5}+22a^{4}+20a^{3}-65a^{2}-13a+32\right){x}-14a^{5}+39a^{4}+35a^{3}-116a^{2}-22a+59$ |
| 1.1-a8 |
1.1-a |
$8$ |
$12$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$4553.484644$ |
1.26451 |
\( -22392918326848 a^{5} + 62312545214048 a^{4} + 58326988617984 a^{3} - 188861213679136 a^{2} - 41041470831552 a + 103045860061712 \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 7 a^{2} + 4 a - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 2\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a\) , \( 2 a^{5} - 6 a^{4} + 6 a^{3} + 8 a^{2} - 23 a + 6\) , \( 7 a^{5} - 17 a^{4} - 3 a^{3} + 31 a^{2} - 26 a + 4\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+7a^{2}+4a-2\right){x}{y}+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-3a-2\right){x}^{2}+\left(2a^{5}-6a^{4}+6a^{3}+8a^{2}-23a+6\right){x}+7a^{5}-17a^{4}-3a^{3}+31a^{2}-26a+4$ |
| 1.1-b1 |
1.1-b |
$8$ |
$20$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 5$ |
2B, 3Ns, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$5.018749737$ |
0.871070 |
\( 226234148706349446880 a^{5} - 678702446119048340640 a^{4} - 787565029867649528128 a^{3} + 2144969922105746209408 a^{2} + 1457758494777550796864 a - 408593223393278574256 \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 4 a - 3\) , \( -345 a^{5} + 931 a^{4} + 1292 a^{3} - 2941 a^{2} - 2050 a + 568\) , \( -6492 a^{5} + 17044 a^{4} + 23992 a^{3} - 52088 a^{2} - 37541 a + 10336\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+4a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-345a^{5}+931a^{4}+1292a^{3}-2941a^{2}-2050a+568\right){x}-6492a^{5}+17044a^{4}+23992a^{3}-52088a^{2}-37541a+10336$ |
| 1.1-b2 |
1.1-b |
$8$ |
$20$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 5$ |
2B, 3Ns, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$5.018749737$ |
0.871070 |
\( 226234148706349446880 a^{4} - 452468297412698893760 a^{3} - 117371564957748259392 a^{2} + 343605713664097706272 a - 64987509729180867984 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 6 a^{3} + 14 a^{2} + 5 a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 7 a^{2} + 4 a - 3\) , \( -705 a^{5} + 2053 a^{4} + 1106 a^{3} - 4760 a^{2} + 53 a + 199\) , \( -13385 a^{5} + 40482 a^{4} + 16374 a^{3} - 91697 a^{2} + 11320 a + 1618\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-6a^{3}+14a^{2}+5a-4\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+7a^{2}+4a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-705a^{5}+2053a^{4}+1106a^{3}-4760a^{2}+53a+199\right){x}-13385a^{5}+40482a^{4}+16374a^{3}-91697a^{2}+11320a+1618$ |
| 1.1-b3 |
1.1-b |
$8$ |
$20$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3, 5$ |
2Cs, 3Ns, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$313671.8586$ |
0.871070 |
\( 4096 \) |
\( \bigl[0\) , \( -2 a^{5} + 5 a^{4} + 4 a^{3} - 11 a^{2} - a\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 7 a - 3\) , \( -12 a^{5} + 25 a^{4} + 52 a^{3} - 73 a^{2} - 74 a + 19\) , \( 54 a^{5} - 119 a^{4} - 205 a^{3} + 327 a^{2} + 265 a - 71\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+7a-3\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+4a^{3}-11a^{2}-a\right){x}^{2}+\left(-12a^{5}+25a^{4}+52a^{3}-73a^{2}-74a+19\right){x}+54a^{5}-119a^{4}-205a^{3}+327a^{2}+265a-71$ |
| 1.1-b4 |
1.1-b |
$8$ |
$20$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 5$ |
2B, 3Ns, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$78417.96465$ |
0.871070 |
\( -1597472 a^{5} + 3194944 a^{4} + 2932864 a^{3} - 2670784 a^{2} - 1073312 a + 340816 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 13 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + a + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 7 a^{2} + 4 a - 3\) , \( 2 a^{5} - 7 a^{4} + 3 a^{3} + 6 a^{2} - 5 a + 3\) , \( -2 a^{5} + 8 a^{4} - 9 a^{3} - 2 a^{2} + 11 a - 2\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+13a^{2}+2a-2\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+7a^{2}+4a-3\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-9a^{2}+a+3\right){x}^{2}+\left(2a^{5}-7a^{4}+3a^{3}+6a^{2}-5a+3\right){x}-2a^{5}+8a^{4}-9a^{3}-2a^{2}+11a-2$ |
| 1.1-b5 |
1.1-b |
$8$ |
$20$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 5$ |
2B, 3Ns, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$78417.96465$ |
0.871070 |
\( 1597472 a^{5} - 4792416 a^{4} + 262080 a^{3} + 9322752 a^{2} - 7176128 a + 1127056 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 4 a - 4\) , \( -a - 1\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 16 a^{2} + 7 a - 6\) , \( a^{3} - a^{2} - 5 a - 3\) , \( 2 a^{5} - 2 a^{4} - 6 a^{3} + a^{2} - 3\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+4a-4\right){x}{y}+\left(2a^{5}-5a^{4}-7a^{3}+16a^{2}+7a-6\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a^{3}-a^{2}-5a-3\right){x}+2a^{5}-2a^{4}-6a^{3}+a^{2}-3$ |
| 1.1-b6 |
1.1-b |
$8$ |
$20$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 5$ |
2B, 3Ns, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$78417.96465$ |
0.871070 |
\( 1597472 a^{4} - 3194944 a^{3} - 6651968 a^{2} + 8249440 a + 9376496 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 16 a^{2} + 7 a - 6\) , \( -a^{4} + a^{3} + 3 a^{2} + a - 2\) , \( -3 a^{5} + 6 a^{4} + 12 a^{3} - 19 a^{2} - 11 a + 8\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(2a^{5}-5a^{4}-7a^{3}+16a^{2}+7a-6\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-a^{4}+a^{3}+3a^{2}+a-2\right){x}-3a^{5}+6a^{4}+12a^{3}-19a^{2}-11a+8$ |
| 1.1-b7 |
1.1-b |
$8$ |
$20$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3, 5$ |
2Cs, 3Ns, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$20.07499895$ |
0.871070 |
\( 38477541376 \) |
\( \bigl[0\) , \( -a^{4} + a^{3} + 3 a^{2} + a\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a\) , \( 843 a^{5} - 2250 a^{4} - 2247 a^{3} + 6613 a^{2} + 1547 a - 3587\) , \( 17103 a^{5} - 46342 a^{4} - 45500 a^{3} + 138496 a^{2} + 31589 a - 75387\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+2a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}+a\right){x}^{2}+\left(843a^{5}-2250a^{4}-2247a^{3}+6613a^{2}+1547a-3587\right){x}+17103a^{5}-46342a^{4}-45500a^{3}+138496a^{2}+31589a-75387$ |
| 1.1-b8 |
1.1-b |
$8$ |
$20$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 5$ |
2B, 3Ns, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$5.018749737$ |
0.871070 |
\( -226234148706349446880 a^{5} + 452468297412698893760 a^{4} + 1240033327280348421888 a^{3} - 2027598357147997950016 a^{2} - 1801364208441648503136 a + 1954101866209670010128 \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} + a - 2\) , \( a^{4} - 4 a^{3} + a^{2} + 7 a - 2\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + 2 a - 2\) , \( 358 a^{5} - 953 a^{4} - 961 a^{3} + 2790 a^{2} + 658 a - 1516\) , \( 4744 a^{5} - 12786 a^{4} - 12634 a^{3} + 37891 a^{2} + 8714 a - 20587\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+9a^{2}+a-2\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+2a-2\right){y}={x}^{3}+\left(a^{4}-4a^{3}+a^{2}+7a-2\right){x}^{2}+\left(358a^{5}-953a^{4}-961a^{3}+2790a^{2}+658a-1516\right){x}+4744a^{5}-12786a^{4}-12634a^{3}+37891a^{2}+8714a-20587$ |
| 16.1-a1 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( 18217531165593504902890968 a^{5} - 10354298909167436993288432 a^{4} - 61612885778130277715028258 a^{3} + 14138041482712268478468030 a^{2} + 34378485251389345189342022 a - 7491901095943595127519592 \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 7 a^{2} + 4 a - 2\) , \( -a^{5} + 2 a^{4} + 6 a^{3} - 9 a^{2} - 10 a + 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( -126 a^{5} + 274 a^{4} + 493 a^{3} - 767 a^{2} - 650 a + 171\) , \( 1202 a^{5} - 2869 a^{4} - 3880 a^{3} + 7530 a^{2} + 4386 a - 1265\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+7a^{2}+4a-2\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+6a^{3}-9a^{2}-10a+4\right){x}^{2}+\left(-126a^{5}+274a^{4}+493a^{3}-767a^{2}-650a+171\right){x}+1202a^{5}-2869a^{4}-3880a^{3}+7530a^{2}+4386a-1265$ |
| 16.1-a2 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( -67856848877915096 a^{5} + 300716409780033264 a^{4} - 294800885744159454 a^{3} - 188665717005740990 a^{2} + 270099449901906106 a - 47398302862808776 \) |
\( \bigl[a^{2} - a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a + 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 7 a - 4\) , \( -11 a^{5} + 6 a^{4} + 41 a^{3} - 28 a^{2} - 19 a + 20\) , \( 78 a^{5} - 59 a^{4} - 208 a^{3} + 63 a^{2} + 102 a - 25\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+7a-4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+a+1\right){x}^{2}+\left(-11a^{5}+6a^{4}+41a^{3}-28a^{2}-19a+20\right){x}+78a^{5}-59a^{4}-208a^{3}+63a^{2}+102a-25$ |
| 16.1-a3 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( 4798284723298476 a^{5} - 10639285742313780 a^{4} - 17923829691220420 a^{3} + 29155764138148604 a^{2} + 22819918697464076 a - 6130506398490252 \) |
\( \bigl[a^{2} - a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a + 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + 2 a - 1\) , \( -9 a^{5} + 18 a^{4} + 33 a^{3} - 47 a^{2} - 40 a + 11\) , \( -28 a^{5} + 65 a^{4} + 102 a^{3} - 179 a^{2} - 131 a + 39\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+2a-1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+a+1\right){x}^{2}+\left(-9a^{5}+18a^{4}+33a^{3}-47a^{2}-40a+11\right){x}-28a^{5}+65a^{4}+102a^{3}-179a^{2}-131a+39$ |
| 16.1-a4 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( 848815008660 a^{5} - 482240870796 a^{4} - 2871148309372 a^{3} + 658634278340 a^{2} + 1602111240116 a - 349129927396 \) |
\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} + a - 2\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 12 a^{2} - 2 a + 3\) , \( 0\) , \( 484 a^{5} - 1352 a^{4} - 1254 a^{3} + 4106 a^{2} + 881 a - 2244\) , \( 3583 a^{5} - 9977 a^{4} - 9325 a^{3} + 30248 a^{2} + 6561 a - 16506\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-2a^{3}+9a^{2}+a-2\right){x}{y}={x}^{3}+\left(-2a^{5}+5a^{4}+5a^{3}-12a^{2}-2a+3\right){x}^{2}+\left(484a^{5}-1352a^{4}-1254a^{3}+4106a^{2}+881a-2244\right){x}+3583a^{5}-9977a^{4}-9325a^{3}+30248a^{2}+6561a-16506$ |
| 16.1-a5 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( -249852480 a^{5} + 1107257536 a^{4} - 1085481152 a^{3} - 694682304 a^{2} + 994528576 a - 174521792 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 7 a - 4\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 6 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 10 a^{5} - 20 a^{4} - 45 a^{3} + 59 a^{2} + 65 a - 15\) , \( -5 a^{5} + 6 a^{4} + 34 a^{3} - 25 a^{2} - 58 a + 13\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+7a-4\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-6a\right){x}^{2}+\left(10a^{5}-20a^{4}-45a^{3}+59a^{2}+65a-15\right){x}-5a^{5}+6a^{4}+34a^{3}-25a^{2}-58a+13$ |
| 16.1-a6 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( 35521312 a^{5} - 78445280 a^{4} - 132657536 a^{3} + 214823360 a^{2} + 168478720 a - 45157600 \) |
\( \bigl[a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( -a^{4} + 3 a^{3} + a^{2} - 7 a + 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 7 a - 4\) , \( 25 a^{5} - 74 a^{4} - 51 a^{3} + 211 a^{2} + 15 a - 98\) , \( -70 a^{5} + 192 a^{4} + 192 a^{3} - 591 a^{2} - 149 a + 332\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+7a-4\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+a^{2}-7a+2\right){x}^{2}+\left(25a^{5}-74a^{4}-51a^{3}+211a^{2}+15a-98\right){x}-70a^{5}+192a^{4}+192a^{3}-591a^{2}-149a+332$ |
| 16.1-a7 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( -14137440 a^{5} + 14293664 a^{4} + 60647168 a^{3} - 14509760 a^{2} - 37983104 a + 8328864 \) |
\( \bigl[a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + a + 1\) , \( 2 a^{5} - 5 a^{4} - 6 a^{3} + 15 a^{2} + 4 a - 5\) , \( 3 a^{5} - 11 a^{4} + 11 a^{3} + 2 a^{2} - 7 a\) , \( -10 a^{5} + 47 a^{4} - 49 a^{3} - 28 a^{2} + 44 a - 11\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){x}{y}+\left(2a^{5}-5a^{4}-6a^{3}+15a^{2}+4a-5\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+a+1\right){x}^{2}+\left(3a^{5}-11a^{4}+11a^{3}+2a^{2}-7a\right){x}-10a^{5}+47a^{4}-49a^{3}-28a^{2}+44a-11$ |
| 16.1-a8 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( -1646025280 a^{5} + 4580375744 a^{4} + 4287416640 a^{3} - 13882519744 a^{2} - 3016824000 a + 7574531136 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 6 a^{3} + 15 a^{2} + 4 a - 5\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 15 a^{2} + 7 a - 5\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 4 a^{5} - 9 a^{4} - 19 a^{3} + 33 a^{2} + 25 a - 9\) , \( 3 a^{5} - 5 a^{4} - 16 a^{3} + 17 a^{2} + 20 a - 2\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-6a^{3}+15a^{2}+4a-5\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-7a^{3}+15a^{2}+7a-5\right){x}^{2}+\left(4a^{5}-9a^{4}-19a^{3}+33a^{2}+25a-9\right){x}+3a^{5}-5a^{4}-16a^{3}+17a^{2}+20a-2$ |
| 16.1-a9 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( 2312562203412 a^{5} - 9001890765420 a^{4} + 3409586459604 a^{3} + 17771190843860 a^{2} - 15862934539100 a + 2593229989260 \) |
\( \bigl[-a^{3} + 2 a^{2} + 2 a - 1\) , \( -2 a^{5} + 5 a^{4} + 7 a^{3} - 15 a^{2} - 8 a + 6\) , \( 2 a^{5} - 5 a^{4} - 6 a^{3} + 15 a^{2} + 4 a - 5\) , \( -34 a^{5} + 133 a^{4} - 51 a^{3} - 265 a^{2} + 239 a - 38\) , \( 236 a^{5} - 917 a^{4} + 343 a^{3} + 1812 a^{2} - 1606 a + 256\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+2a-1\right){x}{y}+\left(2a^{5}-5a^{4}-6a^{3}+15a^{2}+4a-5\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+7a^{3}-15a^{2}-8a+6\right){x}^{2}+\left(-34a^{5}+133a^{4}-51a^{3}-265a^{2}+239a-38\right){x}+236a^{5}-917a^{4}+343a^{3}+1812a^{2}-1606a+256$ |
| 16.1-a10 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( -1984510087077588 a^{5} + 2197961833651116 a^{4} + 8128533457322220 a^{3} - 2477820086925076 a^{2} - 4689128540653028 a + 1048650919699204 \) |
\( \bigl[-a^{3} + 2 a^{2} + 2 a - 1\) , \( -2 a^{5} + 5 a^{4} + 7 a^{3} - 15 a^{2} - 8 a + 6\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + 2 a - 1\) , \( a^{5} + 7 a^{4} - 19 a^{3} - 20 a^{2} + 26 a\) , \( 12 a^{5} - 17 a^{4} - 39 a^{3} + 20 a^{2} + 6 a\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+2a-1\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+8a^{2}+2a-1\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+7a^{3}-15a^{2}-8a+6\right){x}^{2}+\left(a^{5}+7a^{4}-19a^{3}-20a^{2}+26a\right){x}+12a^{5}-17a^{4}-39a^{3}+20a^{2}+6a$ |
| 16.1-a11 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( -447037782324829748 a^{5} + 1243967483828201268 a^{4} + 1164402376837563790 a^{3} - 3770303561304132410 a^{2} - 819325398371139738 a + 2057141199588276648 \) |
\( \bigl[-a^{3} + 2 a^{2} + 2 a - 1\) , \( -2 a^{5} + 5 a^{4} + 7 a^{3} - 15 a^{2} - 8 a + 6\) , \( 2 a^{5} - 5 a^{4} - 6 a^{3} + 15 a^{2} + 4 a - 5\) , \( -34 a^{5} + 128 a^{4} - 46 a^{3} - 235 a^{2} + 219 a - 73\) , \( 305 a^{5} - 1091 a^{4} + 127 a^{3} + 2320 a^{2} - 1387 a + 43\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+2a-1\right){x}{y}+\left(2a^{5}-5a^{4}-6a^{3}+15a^{2}+4a-5\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+7a^{3}-15a^{2}-8a+6\right){x}^{2}+\left(-34a^{5}+128a^{4}-46a^{3}-235a^{2}+219a-73\right){x}+305a^{5}-1091a^{4}+127a^{3}+2320a^{2}-1387a+43$ |
| 16.1-a12 |
16.1-a |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( 49637219981665464197112884 a^{5} - 193209954532609470306723124 a^{4} + 73154062001651386765697650 a^{3} + 381449289177320437070885690 a^{2} - 340421018510988548741365606 a + 55619604105418652829948456 \) |
\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 4 a - 4\) , \( a^{4} - 4 a^{3} + a^{2} + 8 a - 2\) , \( a^{2} - a - 1\) , \( 641 a^{5} - 1784 a^{4} - 1665 a^{3} + 5406 a^{2} + 1155 a - 2957\) , \( 13016 a^{5} - 36180 a^{4} - 33980 a^{3} + 109614 a^{2} + 24050 a - 59675\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+4a-4\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{4}-4a^{3}+a^{2}+8a-2\right){x}^{2}+\left(641a^{5}-1784a^{4}-1665a^{3}+5406a^{2}+1155a-2957\right){x}+13016a^{5}-36180a^{4}-33980a^{3}+109614a^{2}+24050a-59675$ |
| 16.1-b1 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( -18217531165593504902890968 a^{5} + 80733356918800087521166408 a^{4} - 79145230241135023340727694 a^{3} - 50651097650748137597437656 a^{2} + 72513628926279174457505580 a - 12725027883546191265135262 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 7 a^{3} + 16 a^{2} + 7 a - 5\) , \( -a^{2} + a + 2\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( 1098 a^{5} - 3067 a^{4} - 2839 a^{3} + 9253 a^{2} + 2016 a - 5026\) , \( -20935 a^{5} + 58242 a^{4} + 54455 a^{3} - 176397 a^{2} - 38277 a + 96240\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-7a^{3}+16a^{2}+7a-5\right){x}{y}+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(1098a^{5}-3067a^{4}-2839a^{3}+9253a^{2}+2016a-5026\right){x}-20935a^{5}+58242a^{4}+54455a^{3}-176397a^{2}-38277a+96240$ |
| 16.1-b2 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( 447037782324829748 a^{5} - 991221427795947472 a^{4} - 1669894488902071382 a^{3} + 2716330648929469088 a^{2} + 2126044366778056856 a - 571155681746060190 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 16 a^{2} + 7 a - 7\) , \( 2 a^{5} - 5 a^{4} - 6 a^{3} + 15 a^{2} + 4 a - 5\) , \( 33 a^{5} - 38 a^{4} - 126 a^{3} + 44 a^{2} + 51 a - 37\) , \( -305 a^{5} + 434 a^{4} + 1187 a^{3} - 795 a^{2} - 793 a + 316\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(2a^{5}-5a^{4}-6a^{3}+15a^{2}+4a-5\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-7a^{3}+16a^{2}+7a-7\right){x}^{2}+\left(33a^{5}-38a^{4}-126a^{3}+44a^{2}+51a-37\right){x}-305a^{5}+434a^{4}+1187a^{3}-795a^{2}-793a+316$ |
| 16.1-b3 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( 67856848877915096 a^{5} - 38567834609542216 a^{4} - 229496264596822642 a^{3} + 52661595662829272 a^{2} + 128053246611496660 a - 27905894808684946 \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 3 a + 2\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( 12 a^{5} - 51 a^{4} + 40 a^{3} + 29 a^{2} - 12 a + 5\) , \( -79 a^{5} + 334 a^{4} - 335 a^{3} - 142 a^{2} + 243 a - 46\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+3a+2\right){x}^{2}+\left(12a^{5}-51a^{4}+40a^{3}+29a^{2}-12a+5\right){x}-79a^{5}+334a^{4}-335a^{3}-142a^{2}+243a-46$ |
| 16.1-b4 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( -848815008660 a^{5} + 3761834172504 a^{4} - 3688038294044 a^{3} - 2360105787952 a^{2} + 3378953571204 a - 592958580448 \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 6 a + 3\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 16 a^{2} + 7 a - 5\) , \( -22 a^{5} + 62 a^{4} + 44 a^{3} - 146 a^{2} - 21 a + 3\) , \( 5 a^{5} - 52 a^{4} + 110 a^{3} + 73 a^{2} - 264 a + 37\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){x}{y}+\left(2a^{5}-5a^{4}-7a^{3}+16a^{2}+7a-5\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+5a^{3}-7a^{2}-6a+3\right){x}^{2}+\left(-22a^{5}+62a^{4}+44a^{3}-146a^{2}-21a+3\right){x}+5a^{5}-52a^{4}+110a^{3}+73a^{2}-264a+37$ |
| 16.1-b5 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( 1646025280 a^{5} - 3649750656 a^{4} - 6148666816 a^{3} + 10001731840 a^{2} + 7828236992 a - 2103045504 \) |
\( \bigl[a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( -a^{5} + 3 a^{4} + 4 a^{3} - 11 a^{2} - 6 a + 6\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} + a - 2\) , \( -4 a^{5} + 7 a^{4} + 18 a^{3} - 20 a^{2} - 20 a + 11\) , \( 8 a^{5} - 13 a^{4} - 28 a^{3} + 24 a^{2} + 18 a - 2\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){x}{y}+\left(a^{5}-3a^{4}-2a^{3}+9a^{2}+a-2\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+4a^{3}-11a^{2}-6a+6\right){x}^{2}+\left(-4a^{5}+7a^{4}+18a^{3}-20a^{2}-20a+11\right){x}+8a^{5}-13a^{4}-28a^{3}+24a^{2}+18a-2$ |
| 16.1-b6 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( 249852480 a^{5} - 142004864 a^{4} - 845024192 a^{3} + 193894656 a^{2} + 471511744 a - 102751616 \) |
\( \bigl[a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( -a^{4} + 2 a^{3} + a^{2} - 3 a + 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( -3 a^{5} + 5 a^{4} + 16 a^{3} - 20 a^{2} - 24 a + 16\) , \( -a^{5} + a^{4} + 9 a^{3} - 8 a^{2} - 16 a + 9\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+a^{2}-3a+2\right){x}^{2}+\left(-3a^{5}+5a^{4}+16a^{3}-20a^{2}-24a+16\right){x}-a^{5}+a^{4}+9a^{3}-8a^{2}-16a+9$ |
| 16.1-b7 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( 14137440 a^{5} - 56393536 a^{4} + 23552576 a^{3} + 111819328 a^{2} - 101426336 a + 16639392 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 6 a^{3} + 15 a^{2} + 4 a - 5\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 2 a + 1\) , \( 2 a^{5} - 5 a^{4} - 6 a^{3} + 15 a^{2} + 4 a - 5\) , \( 40 a^{5} - 112 a^{4} - 104 a^{3} + 341 a^{2} + 74 a - 191\) , \( 52 a^{5} - 145 a^{4} - 135 a^{3} + 440 a^{2} + 95 a - 243\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-6a^{3}+15a^{2}+4a-5\right){x}{y}+\left(2a^{5}-5a^{4}-6a^{3}+15a^{2}+4a-5\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+2a+1\right){x}^{2}+\left(40a^{5}-112a^{4}-104a^{3}+341a^{2}+74a-191\right){x}+52a^{5}-145a^{4}-135a^{3}+440a^{2}+95a-243$ |
| 16.1-b8 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( -35521312 a^{5} + 99161280 a^{4} + 91225536 a^{3} - 298607808 a^{2} - 63978272 a + 162562976 \) |
\( \bigl[a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 2\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( -19 a^{5} + 70 a^{4} - 19 a^{3} - 139 a^{2} + 113 a - 18\) , \( -22 a^{5} + 85 a^{4} - 32 a^{3} - 167 a^{2} + 151 a - 25\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){x}{y}+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-2\right){x}^{2}+\left(-19a^{5}+70a^{4}-19a^{3}-139a^{2}+113a-18\right){x}-22a^{5}+85a^{4}-32a^{3}-167a^{2}+151a-25$ |
| 16.1-b9 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( -2312562203412 a^{5} + 2560920251640 a^{4} + 9472354567956 a^{3} - 2885772335728 a^{2} - 5463454482812 a + 1221744191616 \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 4 a - 4\) , \( 20 a^{5} - 57 a^{4} - 59 a^{3} + 176 a^{2} + 56 a - 93\) , \( -57 a^{5} + 156 a^{4} + 140 a^{3} - 467 a^{2} - 81 a + 254\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+4a-4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+4a\right){x}^{2}+\left(20a^{5}-57a^{4}-59a^{3}+176a^{2}+56a-93\right){x}-57a^{5}+156a^{4}+140a^{3}-467a^{2}-81a+254$ |
| 16.1-b10 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( 1984510087077588 a^{5} - 7724588601736824 a^{4} + 2924720078849196 a^{3} + 15250450416172400 a^{2} - 13610128556680004 a + 2223687496016848 \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( 12 a^{5} - 18 a^{4} - 41 a^{3} + 24 a^{2} + 24 a - 7\) , \( -21 a^{5} + 25 a^{4} + 94 a^{3} - 49 a^{2} - 70 a + 16\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-3a\right){x}^{2}+\left(12a^{5}-18a^{4}-41a^{3}+24a^{2}+24a-7\right){x}-21a^{5}+25a^{4}+94a^{3}-49a^{2}-70a+16$ |
| 16.1-b11 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( -4798284723298476 a^{5} + 13352137874178600 a^{4} + 12498125427490780 a^{3} - 40468592156410576 a^{2} - 8794238547337284 a + 22080345726886704 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + a + 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( 5 a^{5} - 17 a^{4} + 9 a^{3} + 9 a^{2} - 9 a + 3\) , \( -5 a^{5} + 27 a^{4} - 33 a^{3} - 21 a^{2} + 26 a - 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+a+2\right){x}^{2}+\left(5a^{5}-17a^{4}+9a^{3}+9a^{2}-9a+3\right){x}-5a^{5}+27a^{4}-33a^{3}-21a^{2}+26a-4$ |
| 16.1-b12 |
16.1-b |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( -49637219981665464197112884 a^{5} + 54976145375717850678841296 a^{4} + 203313556312131852490066006 a^{3} - 61976052196727582501231264 a^{2} - 117286027626495925456170648 a + 26229202222457921815555950 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 13 a^{2} + 2 a - 2\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} - a + 4\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 4 a - 4\) , \( -56 a^{5} + 214 a^{4} - 77 a^{3} - 411 a^{2} + 364 a - 69\) , \( 260 a^{5} - 1011 a^{4} + 340 a^{3} + 2193 a^{2} - 2062 a + 399\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+13a^{2}+2a-2\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+4a-4\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}-a+4\right){x}^{2}+\left(-56a^{5}+214a^{4}-77a^{3}-411a^{2}+364a-69\right){x}+260a^{5}-1011a^{4}+340a^{3}+2193a^{2}-2062a+399$ |
| 16.1-c1 |
16.1-c |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( 120016277991298114724990860 a^{5} - 266113319404615802262475224 a^{4} - 448316732182626585482608284 a^{3} + 729253576125018218661041398 a^{2} + 570779323199449522322285578 a - 153338245379616227855058406 \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a - 1\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 3 a - 4\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 16 a^{2} + 7 a - 5\) , \( -29 a^{5} + 36 a^{4} + 94 a^{3} - 95 a^{2} - 57 a + 49\) , \( -129 a^{5} + 666 a^{4} + 213 a^{3} - 2121 a^{2} - 218 a + 1148\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+2a-1\right){x}{y}+\left(2a^{5}-5a^{4}-7a^{3}+16a^{2}+7a-5\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+3a-4\right){x}^{2}+\left(-29a^{5}+36a^{4}+94a^{3}-95a^{2}-57a+49\right){x}-129a^{5}+666a^{4}+213a^{3}-2121a^{2}-218a+1148$ |
| 16.1-c2 |
16.1-c |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( -728342044787232 a^{5} + 3227742430078524 a^{4} - 3164248684395272 a^{3} - 2025045195199180 a^{2} + 2899115390393592 a - 508750213837620 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + a + 2\) , \( 2 a^{5} - 5 a^{4} - 6 a^{3} + 14 a^{2} + 5 a - 4\) , \( 19 a^{5} - 55 a^{4} - 46 a^{3} + 171 a^{2} + 25 a - 104\) , \( -51 a^{5} + 139 a^{4} + 135 a^{3} - 408 a^{2} - 102 a + 195\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(2a^{5}-5a^{4}-6a^{3}+14a^{2}+5a-4\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+a^{3}-7a^{2}+a+2\right){x}^{2}+\left(19a^{5}-55a^{4}-46a^{3}+171a^{2}+25a-104\right){x}-51a^{5}+139a^{4}+135a^{3}-408a^{2}-102a+195$ |
| 16.1-c3 |
16.1-c |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( 728342044787232 a^{5} - 413967793857636 a^{4} - 2463300588046504 a^{3} + 565242884213828 a^{2} + 1374461556812648 a - 299528317747188 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 6 a^{3} + 14 a^{2} + 5 a - 4\) , \( a^{4} - 3 a^{3} + 5 a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( -10 a^{5} + 21 a^{4} + 36 a^{3} - 53 a^{2} - 41 a + 12\) , \( 74 a^{5} - 78 a^{4} - 302 a^{3} + 70 a^{2} + 161 a - 35\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-6a^{3}+14a^{2}+5a-4\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){y}={x}^{3}+\left(a^{4}-3a^{3}+5a-1\right){x}^{2}+\left(-10a^{5}+21a^{4}+36a^{3}-53a^{2}-41a+12\right){x}+74a^{5}-78a^{4}-302a^{3}+70a^{2}+161a-35$ |
| 16.1-c4 |
16.1-c |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( 5592155505120 a^{5} - 12399700156764 a^{4} - 20889256265176 a^{3} + 33980233843196 a^{2} + 26595786367640 a - 7144897510780 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 6 a^{3} + 14 a^{2} + 5 a - 4\) , \( 2 a^{3} - 3 a^{2} - 5 a + 4\) , \( 2 a^{5} - 5 a^{4} - 6 a^{3} + 14 a^{2} + 5 a - 4\) , \( -4 a^{5} + 10 a^{4} + 14 a^{3} - 42 a^{2} + 12 a + 2\) , \( -29 a^{5} + 114 a^{4} - 61 a^{3} - 171 a^{2} + 154 a - 24\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-6a^{3}+14a^{2}+5a-4\right){x}{y}+\left(2a^{5}-5a^{4}-6a^{3}+14a^{2}+5a-4\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-5a+4\right){x}^{2}+\left(-4a^{5}+10a^{4}+14a^{3}-42a^{2}+12a+2\right){x}-29a^{5}+114a^{4}-61a^{3}-171a^{2}+154a-24$ |
| 16.1-c5 |
16.1-c |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( 6578560 a^{5} - 5754464 a^{4} - 22632128 a^{3} + 11556224 a^{2} + 15800992 a - 3734464 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 7 a - 4\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} - a + 2\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( 6 a^{5} - 30 a^{4} + 34 a^{3} + 22 a^{2} - 38 a + 7\) , \( -8 a^{5} + 34 a^{4} - 31 a^{3} - 23 a^{2} + 31 a - 6\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+7a-4\right){x}{y}+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+5a^{3}-13a^{2}-a+2\right){x}^{2}+\left(6a^{5}-30a^{4}+34a^{3}+22a^{2}-38a+7\right){x}-8a^{5}+34a^{4}-31a^{3}-23a^{2}+31a-6$ |
| 16.1-c6 |
16.1-c |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( -6578560 a^{5} + 27138336 a^{4} - 20135616 a^{3} - 25081344 a^{2} + 19108000 a + 1814720 \) |
\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 7 a - 4\) , \( a^{5} - 3 a^{4} - a^{3} + 6 a^{2} - 2 a\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 7 a - 4\) , \( 42 a^{5} - 119 a^{4} - 104 a^{3} + 356 a^{2} + 66 a - 191\) , \( -188 a^{5} + 522 a^{4} + 493 a^{3} - 1584 a^{2} - 352 a + 864\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+7a-4\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+7a-4\right){y}={x}^{3}+\left(a^{5}-3a^{4}-a^{3}+6a^{2}-2a\right){x}^{2}+\left(42a^{5}-119a^{4}-104a^{3}+356a^{2}+66a-191\right){x}-188a^{5}+522a^{4}+493a^{3}-1584a^{2}-352a+864$ |
| 16.1-c7 |
16.1-c |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( -680772608 a^{5} + 753992640 a^{4} + 2788443776 a^{3} - 849992768 a^{2} - 1608578560 a + 359731776 \) |
\( \bigl[2 a^{5} - 5 a^{4} - 6 a^{3} + 15 a^{2} + 4 a - 5\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{2} - a - 1\) , \( 3 a^{5} - 4 a^{4} - 10 a^{3} + 2 a^{2} + 7 a + 7\) , \( -3 a^{5} + 4 a^{4} + 13 a^{3} - 9 a^{2} - 8 a + 8\bigr] \) |
${y}^2+\left(2a^{5}-5a^{4}-6a^{3}+15a^{2}+4a-5\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(3a^{5}-4a^{4}-10a^{3}+2a^{2}+7a+7\right){x}-3a^{5}+4a^{4}+13a^{3}-9a^{2}-8a+8$ |
| 16.1-c8 |
16.1-c |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( 680772608 a^{5} - 2649870400 a^{4} + 1003311744 a^{3} + 5231568320 a^{2} - 4668874752 a + 762824256 \) |
\( \bigl[a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( a^{4} - 3 a^{3} + 6 a - 3\) , \( 2 a^{5} - 5 a^{4} - 6 a^{3} + 14 a^{2} + 5 a - 4\) , \( -a^{5} + 6 a^{4} - 4 a^{3} - 11 a^{2} + 6 a - 1\) , \( 2 a^{3} - 7 a\bigr] \) |
${y}^2+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){x}{y}+\left(2a^{5}-5a^{4}-6a^{3}+14a^{2}+5a-4\right){y}={x}^{3}+\left(a^{4}-3a^{3}+6a-3\right){x}^{2}+\left(-a^{5}+6a^{4}-4a^{3}-11a^{2}+6a-1\right){x}+2a^{3}-7a$ |
| 16.1-c9 |
16.1-c |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B |
$1$ |
\( 1 \) |
$1$ |
$20291.12822$ |
1.40872 |
\( -5592155505120 a^{5} + 15561077368836 a^{4} + 14566501841032 a^{3} - 47164180841716 a^{2} - 10250462157048 a + 25734321783236 \) |
\( \bigl[-a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + a\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - a - 1\) , \( 86 a^{5} - 238 a^{4} - 225 a^{3} + 719 a^{2} + 158 a - 389\) , \( -567 a^{5} + 1579 a^{4} + 1474 a^{3} - 4785 a^{2} - 1033 a + 2608\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+2a-1\right){x}{y}+\left(a^{5}-3a^{4}-a^{3}+7a^{2}-a-1\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+7a^{2}+a\right){x}^{2}+\left(86a^{5}-238a^{4}-225a^{3}+719a^{2}+158a-389\right){x}-567a^{5}+1579a^{4}+1474a^{3}-4785a^{2}-1033a+2608$ |
| 16.1-c10 |
16.1-c |
$12$ |
$24$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$101.35483$ |
$(a^3-a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$1268.195513$ |
1.40872 |
\( -184889207154338700 a^{5} + 204775702284474328 a^{4} + 757304309563018908 a^{3} - 230849018567470326 a^{2} - 436868129442863626 a + 97698787561163702 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 2 a + 4\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 7 a - 4\) , \( -76 a^{5} + 166 a^{4} + 304 a^{3} - 478 a^{2} - 408 a + 104\) , \( 577 a^{5} - 1251 a^{4} - 2201 a^{3} + 3445 a^{2} + 2751 a - 735\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+7a-4\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-2a+4\right){x}^{2}+\left(-76a^{5}+166a^{4}+304a^{3}-478a^{2}-408a+104\right){x}+577a^{5}-1251a^{4}-2201a^{3}+3445a^{2}+2751a-735$ |
*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.
