| 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 |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$8.125829529$ |
1.245930137 |
\( 82350052031814927961883406 a^{3} - 106788930944214300782299912 a^{2} - 380058698488634322797919559 a + 277489450066464824619304156 \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( 0\) , \( -83 a^{3} + 72 a^{2} + 507 a - 343\) , \( -600 a^{3} + 457 a^{2} + 3821 a - 2584\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-83a^{3}+72a^{2}+507a-343\right){x}-600a^{3}+457a^{2}+3821a-2584$ |
| 1.1-a2 |
1.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$16$ |
\( 1 \) |
$1$ |
$130.0132724$ |
1.245930137 |
\( 4231578647872 a^{3} - 5487350054679 a^{2} - 19529495933348 a + 14258909677340 \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( 0\) , \( 17 a^{3} - 58 a^{2} + 47 a - 8\) , \( 183 a^{3} - 550 a^{2} + 179 a + 71\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(17a^{3}-58a^{2}+47a-8\right){x}+183a^{3}-550a^{2}+179a+71$ |
| 1.1-a3 |
1.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$520.0530899$ |
1.245930137 |
\( -1472887 a^{3} - 436851 a^{2} + 8267198 a + 6865599 \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( 0\) , \( 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( 4 a^{3} - 8 a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(2a^{3}-3a^{2}+2a+2\right){x}+4a^{3}-8a^{2}+a+1$ |
| 1.1-a4 |
1.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$520.0530899$ |
1.245930137 |
\( 74 a^{3} + 872 a^{2} - 1691 a - 2022 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 5 a\) , \( 4 a^{3} - 2 a^{2} - 19 a - 1\) , \( 4 a^{3} - a^{2} - 19 a - 5\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(4a^{3}-2a^{2}-19a-1\right){x}+4a^{3}-a^{2}-19a-5$ |
| 1.1-a5 |
1.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$32.50331811$ |
1.245930137 |
\( -4698022885171982 a^{3} + 13884594808158984 a^{2} - 3586632086549177 a - 2410025104920332 \) |
\( \bigl[a\) , \( 0\) , \( a^{3} - a^{2} - 5 a + 2\) , \( -828 a^{3} + 1034 a^{2} + 3955 a - 2870\) , \( -20422 a^{3} + 26113 a^{2} + 95447 a - 69441\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-5a+2\right){y}={x}^{3}+\left(-828a^{3}+1034a^{2}+3955a-2870\right){x}-20422a^{3}+26113a^{2}+95447a-69441$ |
| 1.1-a6 |
1.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$130.0132724$ |
1.245930137 |
\( -28593664633798 a^{3} + 9458072708331 a^{2} + 149297900792702 a + 42726541222934 \) |
\( \bigl[a^{3} - a^{2} - 4 a + 3\) , \( a^{2} - 3\) , \( a^{3} - a^{2} - 5 a + 2\) , \( -31 a^{3} - 43 a^{2} + 37 a + 6\) , \( -352 a^{3} - 554 a^{2} + 328 a + 133\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+3\right){x}{y}+\left(a^{3}-a^{2}-5a+2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-31a^{3}-43a^{2}+37a+6\right){x}-352a^{3}-554a^{2}+328a+133$ |
| 1.1-b1 |
1.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$4.118843094$ |
0.631540536 |
\( 82350052031814927961883406 a^{3} - 106788930944214300782299912 a^{2} - 380058698488634322797919559 a + 277489450066464824619304156 \) |
\( \bigl[a^{2} - a - 3\) , \( -a + 1\) , \( a^{3} - 5 a\) , \( -1198 a^{3} + 1544 a^{2} + 5559 a - 4053\) , \( -35687 a^{3} + 46219 a^{2} + 164889 a - 120350\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1198a^{3}+1544a^{2}+5559a-4053\right){x}-35687a^{3}+46219a^{2}+164889a-120350$ |
| 1.1-b2 |
1.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$16$ |
\( 1 \) |
$1$ |
$65.90148951$ |
0.631540536 |
\( 4231578647872 a^{3} - 5487350054679 a^{2} - 19529495933348 a + 14258909677340 \) |
\( \bigl[a^{2} - a - 3\) , \( -a + 1\) , \( a^{3} - 5 a\) , \( -68 a^{3} + 79 a^{2} + 344 a - 248\) , \( -580 a^{3} + 695 a^{2} + 2861 a - 2054\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-68a^{3}+79a^{2}+344a-248\right){x}-580a^{3}+695a^{2}+2861a-2054$ |
| 1.1-b3 |
1.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$4.118843094$ |
0.631540536 |
\( -4698022885171982 a^{3} + 13884594808158984 a^{2} - 3586632086549177 a - 2410025104920332 \) |
\( \bigl[a^{2} - a - 3\) , \( -a + 1\) , \( a^{3} - 5 a\) , \( 22 a^{3} - 186 a^{2} + 409 a - 203\) , \( 1135 a^{3} - 4365 a^{2} + 4161 a - 1178\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a^{3}-186a^{2}+409a-203\right){x}+1135a^{3}-4365a^{2}+4161a-1178$ |
| 1.1-b4 |
1.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$1054.423832$ |
0.631540536 |
\( -1472887 a^{3} - 436851 a^{2} + 8267198 a + 6865599 \) |
\( \bigl[a^{2} - a - 3\) , \( -a + 1\) , \( a^{3} - 5 a\) , \( -3 a^{3} + 4 a^{2} + 14 a - 13\) , \( -12 a^{3} + 14 a^{2} + 59 a - 44\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a^{3}+4a^{2}+14a-13\right){x}-12a^{3}+14a^{2}+59a-44$ |
| 1.1-b5 |
1.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1054.423832$ |
0.631540536 |
\( -28593664633798 a^{3} + 9458072708331 a^{2} + 149297900792702 a + 42726541222934 \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a\) , \( -8 a^{3} - 3 a^{2} + 21 a - 6\) , \( 11 a^{3} + 44 a^{2} + 25 a - 38\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-8a^{3}-3a^{2}+21a-6\right){x}+11a^{3}+44a^{2}+25a-38$ |
| 1.1-b6 |
1.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$9.32465$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1054.423832$ |
0.631540536 |
\( 74 a^{3} + 872 a^{2} - 1691 a - 2022 \) |
\( \bigl[a^{3} - a^{2} - 5 a + 2\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( 0\) , \( a^{3} + a^{2} - 7 a - 1\) , \( -2 a^{3} + a^{2} + 8 a + 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+2\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(a^{3}+a^{2}-7a-1\right){x}-2a^{3}+a^{2}+8a+2$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$12.09258$ |
$(a^3-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.065211808$ |
$575.4758637$ |
1.438531414 |
\( \frac{18425172573}{2} a^{3} - \frac{54393984731}{2} a^{2} + \frac{14053897935}{2} a + \frac{9433530423}{2} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - a^{2} - 6 a + 3\) , \( a^{2} - 2\) , \( 11 a^{3} - 17 a^{2} - 34 a + 4\) , \( -14 a^{3} + 26 a^{2} + 19 a + 13\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+3\right){x}^{2}+\left(11a^{3}-17a^{2}-34a+4\right){x}-14a^{3}+26a^{2}+19a+13$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$12.09258$ |
$(a^3-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$76.91707143$ |
0.737103955 |
\( \frac{20848591}{8} a^{3} - \frac{57331317}{4} a^{2} + \frac{137105709}{8} a + \frac{25666015}{4} \) |
\( \bigl[a^{3} - 5 a\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{3} - 6 a\) , \( a^{3} - a^{2} - a\) , \( -3 a^{3} + 4 a^{2} + 18 a - 15\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a^{3}-6a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(a^{3}-a^{2}-a\right){x}-3a^{3}+4a^{2}+18a-15$ |
| 8.1-c1 |
8.1-c |
$2$ |
$3$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$12.09258$ |
$(a^3-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$12.15474123$ |
1.048320860 |
\( -\frac{10985287928341}{8} a^{3} + \frac{904082173847}{2} a^{2} + \frac{14329800495449}{2} a + \frac{16404902742495}{8} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( -a^{3} + a^{2} + 6 a - 3\) , \( a^{3} - a^{2} - 5 a + 2\) , \( 9 a^{3} - 13 a^{2} - 66 a - 9\) , \( 9 a^{3} - 43 a^{2} - 153 a - 69\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{3}-a^{2}-5a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-3\right){x}^{2}+\left(9a^{3}-13a^{2}-66a-9\right){x}+9a^{3}-43a^{2}-153a-69$ |
| 8.1-c2 |
8.1-c |
$2$ |
$3$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$12.09258$ |
$(a^3-3a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$984.5340400$ |
1.048320860 |
\( -\frac{8901}{2} a^{3} + \frac{2975}{2} a^{2} + 22987 a + 4831 \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( -a^{3} + a^{2} + 6 a - 3\) , \( a^{3} - a^{2} - 5 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{3}-a^{2}-5a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-3\right){x}^{2}+\left(-a^{3}+2a^{2}+4a-4\right){x}-1$ |
| 8.1-d1 |
8.1-d |
$1$ |
$1$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$12.09258$ |
$(a^3-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.015879727$ |
$643.4733009$ |
1.175062150 |
\( -14780523 a^{3} + \frac{153565143}{8} a^{2} + 68253318 a - \frac{398739767}{8} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 2\) , \( a\) , \( 5 a + 1\) , \( 2 a^{3} - 3 a^{2} - a\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(5a+1\right){x}+2a^{3}-3a^{2}-a$ |
| 8.1-e1 |
8.1-e |
$1$ |
$1$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$12.09258$ |
$(a^3-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$372.0493169$ |
3.565385653 |
\( -14780523 a^{3} + \frac{153565143}{8} a^{2} + 68253318 a - \frac{398739767}{8} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 3\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{3} - 6 a\) , \( -2 a^{3} + a^{2} + 12 a - 1\) , \( -a^{2} + 2 a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+3\right){x}{y}+\left(a^{3}-6a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-2a^{3}+a^{2}+12a-1\right){x}-a^{2}+2a$ |
| 8.1-f1 |
8.1-f |
$2$ |
$3$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$12.09258$ |
$(a^3-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.013615571$ |
$3937.253293$ |
2.054921429 |
\( -\frac{8901}{2} a^{3} + \frac{2975}{2} a^{2} + 22987 a + 4831 \) |
\( \bigl[a^{3} - a^{2} - 5 a + 3\) , \( -a^{3} + 5 a + 2\) , \( a^{3} - a^{2} - 4 a + 3\) , \( -2 a^{3} + 9 a + 3\) , \( a^{2} + 3 a + 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+3\right){x}{y}+\left(a^{3}-a^{2}-4a+3\right){y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(-2a^{3}+9a+3\right){x}+a^{2}+3a+2$ |
| 8.1-f2 |
8.1-f |
$2$ |
$3$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$12.09258$ |
$(a^3-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.040846714$ |
$437.4725881$ |
2.054921429 |
\( -\frac{10985287928341}{8} a^{3} + \frac{904082173847}{2} a^{2} + \frac{14329800495449}{2} a + \frac{16404902742495}{8} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 3\) , \( -a^{3} + 5 a + 2\) , \( a^{3} - a^{2} - 4 a + 3\) , \( -27 a^{3} - 50 a^{2} + 9 a + 8\) , \( 348 a^{3} + 552 a^{2} - 315 a - 130\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+3\right){x}{y}+\left(a^{3}-a^{2}-4a+3\right){y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(-27a^{3}-50a^{2}+9a+8\right){x}+348a^{3}+552a^{2}-315a-130$ |
| 8.1-g1 |
8.1-g |
$1$ |
$1$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$12.09258$ |
$(a^3-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.427633570$ |
$90.57732543$ |
4.454290439 |
\( \frac{20848591}{8} a^{3} - \frac{57331317}{4} a^{2} + \frac{137105709}{8} a + \frac{25666015}{4} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{2} + 4\) , \( a^{3} - a^{2} - 5 a + 2\) , \( 2 a^{3} - 5 a^{2} - 4 a + 9\) , \( 3 a^{3} - 9 a^{2} + 3 a + 2\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-5a+2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(2a^{3}-5a^{2}-4a+9\right){x}+3a^{3}-9a^{2}+3a+2$ |
| 8.1-h1 |
8.1-h |
$1$ |
$1$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$12.09258$ |
$(a^3-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$162.6538987$ |
1.558728509 |
\( \frac{18425172573}{2} a^{3} - \frac{54393984731}{2} a^{2} + \frac{14053897935}{2} a + \frac{9433530423}{2} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 3\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( a^{3} - 5 a - 1\) , \( 17 a^{3} - 14 a^{2} - 79 a + 6\) , \( 31 a^{3} - 8 a^{2} - 176 a - 28\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+3\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+4\right){x}^{2}+\left(17a^{3}-14a^{2}-79a+6\right){x}+31a^{3}-8a^{2}-176a-28$ |
| 14.1-a1 |
14.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{8} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1.109601231$ |
$45.02824921$ |
3.830433959 |
\( -\frac{132052758893986755}{92236816} a^{3} + \frac{21874107228363709}{46118408} a^{2} + \frac{689337767575288381}{92236816} a + \frac{197273590459273121}{92236816} \) |
\( \bigl[a^{3} - 6 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -20 a^{3} + 16 a^{2} + 127 a - 92\) , \( -43 a^{3} - 20 a^{2} + 457 a - 309\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-20a^{3}+16a^{2}+127a-92\right){x}-43a^{3}-20a^{2}+457a-309$ |
| 14.1-a2 |
14.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{8} \cdot 7^{4} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.554800615$ |
$720.4519873$ |
3.830433959 |
\( -\frac{10156308195}{614656} a^{3} + \frac{1932332501}{307328} a^{2} + \frac{53871409229}{614656} a + \frac{16864249233}{614656} \) |
\( \bigl[a^{3} - 6 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -5 a^{3} + 6 a^{2} + 22 a - 12\) , \( 6 a^{3} - 10 a^{2} - 22 a + 19\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-5a^{3}+6a^{2}+22a-12\right){x}+6a^{3}-10a^{2}-22a+19$ |
| 14.1-a3 |
14.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{16} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$2.219202462$ |
$2.814265575$ |
3.830433959 |
\( -\frac{214923712255265581976283013}{132931722278404} a^{3} + \frac{317224068276547277595953029}{66465861139202} a^{2} - \frac{163804519569114127964110717}{132931722278404} a - \frac{110106115348997558168173573}{132931722278404} \) |
\( \bigl[a^{3} - 6 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 120 a^{3} - 349 a^{2} + 77 a + 63\) , \( 2081 a^{3} - 6717 a^{2} + 3463 a + 42\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(120a^{3}-349a^{2}+77a+63\right){x}+2081a^{3}-6717a^{2}+3463a+42$ |
| 14.1-a4 |
14.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{4} \cdot 7^{2} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.109601231$ |
$720.4519873$ |
3.830433959 |
\( -\frac{847965}{784} a^{3} + \frac{1431539}{392} a^{2} - \frac{1769197}{784} a + \frac{154367}{784} \) |
\( \bigl[a^{3} - 6 a\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - a^{2} - 5 a + 3\) , \( a^{3} - 6 a - 2\) , \( 27 a^{3} - 8 a^{2} - 142 a - 44\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}-a^{2}-5a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(a^{3}-6a-2\right){x}+27a^{3}-8a^{2}-142a-44$ |
| 14.1-a5 |
14.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{16} \cdot 7^{2} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.277400307$ |
$720.4519873$ |
3.830433959 |
\( \frac{17198704073165}{3211264} a^{3} + \frac{11232184290309}{1605632} a^{2} - \frac{21948649503491}{3211264} a - \frac{520692768767}{3211264} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{3} - 5 a\) , \( 3 a^{3} - 21 a - 6\) , \( -2 a^{3} + a^{2} + 9 a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a^{3}-21a-6\right){x}-2a^{3}+a^{2}+9a+2$ |
| 14.1-a6 |
14.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{4} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$2.219202462$ |
$2.814265575$ |
3.830433959 |
\( -\frac{95179358417704702844187}{9604} a^{3} + \frac{15741481610760652692763}{4802} a^{2} + \frac{496965974535884420520925}{9604} a + \frac{142223280344254765184677}{9604} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 3\) , \( a^{2} - 3\) , \( a^{2} - a - 2\) , \( 98 a^{3} - 287 a^{2} + 54 a + 32\) , \( 2311 a^{3} - 6868 a^{2} + 1761 a + 1157\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(98a^{3}-287a^{2}+54a+32\right){x}+2311a^{3}-6868a^{2}+1761a+1157$ |
| 14.1-b1 |
14.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{4} \cdot 7^{2} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.061612995$ |
$877.2347552$ |
2.071830130 |
\( -\frac{847965}{784} a^{3} + \frac{1431539}{392} a^{2} - \frac{1769197}{784} a + \frac{154367}{784} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 3\) , \( a^{3} - 5 a - 1\) , \( -a^{3} + a^{2} + 3 a + 2\) , \( -8 a^{3} + 3 a^{2} + 40 a + 11\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-a^{3}+a^{2}+3a+2\right){x}-8a^{3}+3a^{2}+40a+11$ |
| 14.1-b2 |
14.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{4} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.492903962$ |
$54.82717220$ |
2.071830130 |
\( -\frac{95179358417704702844187}{9604} a^{3} + \frac{15741481610760652692763}{4802} a^{2} + \frac{496965974535884420520925}{9604} a + \frac{142223280344254765184677}{9604} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( 2 a^{3} - 32 a^{2} + 117 a - 133\) , \( 29 a^{3} - 583 a^{2} + 1566 a - 642\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(2a^{3}-32a^{2}+117a-133\right){x}+29a^{3}-583a^{2}+1566a-642$ |
| 14.1-b3 |
14.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{8} \cdot 7^{4} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.123225990$ |
$877.2347552$ |
2.071830130 |
\( -\frac{10156308195}{614656} a^{3} + \frac{1932332501}{307328} a^{2} + \frac{53871409229}{614656} a + \frac{16864249233}{614656} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( 2 a^{3} - 7 a^{2} + 2 a + 7\) , \( 3 a^{3} - 10 a^{2} + 4 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(2a^{3}-7a^{2}+2a+7\right){x}+3a^{3}-10a^{2}+4a+1$ |
| 14.1-b4 |
14.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{8} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.246451981$ |
$219.3086888$ |
2.071830130 |
\( -\frac{132052758893986755}{92236816} a^{3} + \frac{21874107228363709}{46118408} a^{2} + \frac{689337767575288381}{92236816} a + \frac{197273590459273121}{92236816} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( 27 a^{3} - 82 a^{2} + 27 a + 12\) , \( 253 a^{3} - 757 a^{2} + 225 a + 111\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(27a^{3}-82a^{2}+27a+12\right){x}+253a^{3}-757a^{2}+225a+111$ |
| 14.1-b5 |
14.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{16} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.492903962$ |
$13.70679305$ |
2.071830130 |
\( -\frac{214923712255265581976283013}{132931722278404} a^{3} + \frac{317224068276547277595953029}{66465861139202} a^{2} - \frac{163804519569114127964110717}{132931722278404} a - \frac{110106115348997558168173573}{132931722278404} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 2\) , \( -a^{3} + 6 a + 2\) , \( a^{3} - 6 a - 1\) , \( 52 a^{3} - 116 a^{2} - 75 a + 73\) , \( -13214 a^{3} + 16685 a^{2} + 62449 a - 45306\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+2\right){x}{y}+\left(a^{3}-6a-1\right){y}={x}^{3}+\left(-a^{3}+6a+2\right){x}^{2}+\left(52a^{3}-116a^{2}-75a+73\right){x}-13214a^{3}+16685a^{2}+62449a-45306$ |
| 14.1-b6 |
14.1-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{16} \cdot 7^{2} \) |
$12.96876$ |
$(-a^3+a^2+4a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.246451981$ |
$219.3086888$ |
2.071830130 |
\( \frac{17198704073165}{3211264} a^{3} + \frac{11232184290309}{1605632} a^{2} - \frac{21948649503491}{3211264} a - \frac{520692768767}{3211264} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 3\) , \( -a\) , \( a^{3} - a^{2} - 5 a + 3\) , \( 7 a^{3} - 39 a - 21\) , \( 6 a^{3} - a^{2} - 32 a - 14\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+3\right){x}{y}+\left(a^{3}-a^{2}-5a+3\right){y}={x}^{3}-a{x}^{2}+\left(7a^{3}-39a-21\right){x}+6a^{3}-a^{2}-32a-14$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$13.18705$ |
$(-a^3+a^2+4a), (a^3-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.042320289$ |
$510.0658725$ |
4.137241682 |
\( -\frac{623769}{32} a^{3} + \frac{374951}{16} a^{2} + \frac{3209847}{32} a - \frac{2574861}{32} \) |
\( \bigl[a^{3} - 6 a\) , \( -a^{3} + 2 a^{2} + 4 a - 5\) , \( a^{3} - a^{2} - 5 a + 3\) , \( a^{3} - a^{2} - 11 a + 2\) , \( -4 a^{3} - a^{2} + 3 a - 9\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a^{3}-a^{2}-5a+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-5\right){x}^{2}+\left(a^{3}-a^{2}-11a+2\right){x}-4a^{3}-a^{2}+3a-9$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$13.18705$ |
$(-a^3+a^2+4a), (a^3-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.017039454$ |
$3222.618974$ |
2.104895931 |
\( -\frac{623769}{32} a^{3} + \frac{374951}{16} a^{2} + \frac{3209847}{32} a - \frac{2574861}{32} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 2\) , \( -a^{3} + 5 a + 2\) , \( a\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(a^{3}-a^{2}-5a+2\right){x}+a+1$ |
| 16.2-a1 |
16.2-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.117499859$ |
$641.8869911$ |
2.891092021 |
\( -28593664633798 a^{3} + 9458072708331 a^{2} + 149297900792702 a + 42726541222934 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 6 a + 2\) , \( a^{2} - a - 2\) , \( -7 a^{3} + 9 a^{2} + 28 a - 23\) , \( 2 a^{3} - a^{2} - 5 a + 2\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+2\right){x}^{2}+\left(-7a^{3}+9a^{2}+28a-23\right){x}+2a^{3}-a^{2}-5a+2$ |
| 16.2-a2 |
16.2-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$0.939998878$ |
$20.05896847$ |
2.891092021 |
\( 82350052031814927961883406 a^{3} - 106788930944214300782299912 a^{2} - 380058698488634322797919559 a + 277489450066464824619304156 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 6 a + 2\) , \( a^{3} - 6 a - 1\) , \( -183 a^{3} + 157 a^{2} + 754 a - 494\) , \( 1145 a^{3} - 2491 a^{2} - 6546 a + 5226\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-6a-1\right){y}={x}^{3}+\left(-a^{3}+6a+2\right){x}^{2}+\left(-183a^{3}+157a^{2}+754a-494\right){x}+1145a^{3}-2491a^{2}-6546a+5226$ |
| 16.2-a3 |
16.2-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$0.469999439$ |
$160.4717477$ |
2.891092021 |
\( 4231578647872 a^{3} - 5487350054679 a^{2} - 19529495933348 a + 14258909677340 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 6 a + 2\) , \( a^{3} - 6 a - 1\) , \( -38 a^{3} - 33 a^{2} + 74 a - 19\) , \( -277 a^{3} - 501 a^{2} + 175 a + 187\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-6a-1\right){y}={x}^{3}+\left(-a^{3}+6a+2\right){x}^{2}+\left(-38a^{3}-33a^{2}+74a-19\right){x}-277a^{3}-501a^{2}+175a+187$ |
| 16.2-a4 |
16.2-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.234999719$ |
$1283.773982$ |
2.891092021 |
\( -1472887 a^{3} - 436851 a^{2} + 8267198 a + 6865599 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 6 a + 2\) , \( a^{3} - 6 a - 1\) , \( -3 a^{3} - 3 a^{2} + 9 a + 1\) , \( -4 a^{3} - 8 a^{2} + 2 a + 2\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-6a-1\right){y}={x}^{3}+\left(-a^{3}+6a+2\right){x}^{2}+\left(-3a^{3}-3a^{2}+9a+1\right){x}-4a^{3}-8a^{2}+2a+2$ |
| 16.2-a5 |
16.2-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 2 \) |
$0.939998878$ |
$10.02948423$ |
2.891092021 |
\( -4698022885171982 a^{3} + 13884594808158984 a^{2} - 3586632086549177 a - 2410025104920332 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 6 a + 2\) , \( a^{3} - 6 a - 1\) , \( -453 a^{3} - 703 a^{2} + 434 a + 136\) , \( -18471 a^{3} - 29303 a^{2} + 16888 a + 7208\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-6a-1\right){y}={x}^{3}+\left(-a^{3}+6a+2\right){x}^{2}+\left(-453a^{3}-703a^{2}+434a+136\right){x}-18471a^{3}-29303a^{2}+16888a+7208$ |
| 16.2-a6 |
16.2-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.117499859$ |
$1283.773982$ |
2.891092021 |
\( 74 a^{3} + 872 a^{2} - 1691 a - 2022 \) |
\( \bigl[a^{3} - a^{2} - 5 a + 3\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( a + 1\) , \( 4 a^{3} - a^{2} - 20 a - 6\) , \( -6 a^{3} + 2 a^{2} + 31 a + 9\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-1\right){x}^{2}+\left(4a^{3}-a^{2}-20a-6\right){x}-6a^{3}+2a^{2}+31a+9$ |
| 16.2-b1 |
16.2-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.885963394$ |
$633.1710322$ |
2.687898231 |
\( 74 a^{3} + 872 a^{2} - 1691 a - 2022 \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 4\) , \( a + 1\) , \( 2 a^{3} - 4 a^{2} - 8 a + 10\) , \( 7 a^{3} - 3 a^{2} - 38 a - 4\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(2a^{3}-4a^{2}-8a+10\right){x}+7a^{3}-3a^{2}-38a-4$ |
| 16.2-b2 |
16.2-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.442981697$ |
$633.1710322$ |
2.687898231 |
\( -1472887 a^{3} - 436851 a^{2} + 8267198 a + 6865599 \) |
\( \bigl[a^{3} - 6 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 6\) , \( a^{2} - a - 2\) , \( -8 a^{3} - 25 a^{2} - 10 a + 15\) , \( 60 a^{3} + 100 a^{2} - 50 a - 34\bigr] \) |
${y}^2+\left(a^{3}-6a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-6\right){x}^{2}+\left(-8a^{3}-25a^{2}-10a+15\right){x}+60a^{3}+100a^{2}-50a-34$ |
| 16.2-b3 |
16.2-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.771926789$ |
$39.57318951$ |
2.687898231 |
\( 82350052031814927961883406 a^{3} - 106788930944214300782299912 a^{2} - 380058698488634322797919559 a + 277489450066464824619304156 \) |
\( \bigl[a^{3} - 6 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 6\) , \( a^{2} - a - 2\) , \( -183 a^{3} - 260 a^{2} + 210 a + 35\) , \( 5746 a^{3} + 8876 a^{2} - 5573 a - 1971\bigr] \) |
${y}^2+\left(a^{3}-6a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-6\right){x}^{2}+\left(-183a^{3}-260a^{2}+210a+35\right){x}+5746a^{3}+8876a^{2}-5573a-1971$ |
| 16.2-b4 |
16.2-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.885963394$ |
$316.5855161$ |
2.687898231 |
\( 4231578647872 a^{3} - 5487350054679 a^{2} - 19529495933348 a + 14258909677340 \) |
\( \bigl[a^{3} - 5 a\) , \( a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( -108 a^{3} + 133 a^{2} + 481 a - 367\) , \( 977 a^{3} - 1241 a^{2} - 4483 a + 3245\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-108a^{3}+133a^{2}+481a-367\right){x}+977a^{3}-1241a^{2}-4483a+3245$ |
| 16.2-b5 |
16.2-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.771926789$ |
$79.14637903$ |
2.687898231 |
\( -4698022885171982 a^{3} + 13884594808158984 a^{2} - 3586632086549177 a - 2410025104920332 \) |
\( \bigl[a^{3} - 5 a\) , \( a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( -158 a^{3} + 28 a^{2} + 471 a - 362\) , \( 1833 a^{3} + 214 a^{2} - 5038 a + 2975\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-158a^{3}+28a^{2}+471a-362\right){x}+1833a^{3}+214a^{2}-5038a+2975$ |
| 16.2-b6 |
16.2-b |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$13.18705$ |
$(-a^3+a^2+4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.885963394$ |
$79.14637903$ |
2.687898231 |
\( -28593664633798 a^{3} + 9458072708331 a^{2} + 149297900792702 a + 42726541222934 \) |
\( \bigl[a^{3} - 5 a\) , \( -a^{2} + 4\) , \( 0\) , \( -88 a^{3} + 112 a^{2} + 407 a - 285\) , \( 301 a^{3} - 392 a^{2} - 1388 a + 1021\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-88a^{3}+112a^{2}+407a-285\right){x}+301a^{3}-392a^{2}-1388a+1021$ |
| 22.1-a1 |
22.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{8} \cdot 11^{2} \) |
$13.72257$ |
$(-a^3+a^2+4a), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$79.90695404$ |
3.063025191 |
\( -\frac{313015089543059797675}{30976} a^{3} + \frac{462005416543137736525}{15488} a^{2} - \frac{238565031175609236475}{30976} a - \frac{160358639674713583959}{30976} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + 2 a^{2} + 5 a - 6\) , \( a^{3} - a^{2} - 5 a + 3\) , \( -42 a^{3} + 31 a^{2} + 164 a - 112\) , \( 291 a^{3} + 86 a^{2} - 748 a + 376\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-6\right){x}^{2}+\left(-42a^{3}+31a^{2}+164a-112\right){x}+291a^{3}+86a^{2}-748a+376$ |
| 22.1-a2 |
22.1-a |
$6$ |
$8$ |
4.4.10889.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2 \cdot 11 \) |
$13.72257$ |
$(-a^3+a^2+4a), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$19.97673851$ |
3.063025191 |
\( \frac{432172229107021906425}{22} a^{3} - \frac{280213607589992333639}{11} a^{2} - \frac{1994544154676311492015}{22} a + \frac{1456261790127039987863}{22} \) |
\( \bigl[a^{3} - 6 a\) , \( -a - 1\) , \( a + 1\) , \( -34 a^{3} + 53 a^{2} + 82 a + 18\) , \( 911 a^{3} - 2655 a^{2} + 615 a + 440\bigr] \) |
${y}^2+\left(a^{3}-6a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-34a^{3}+53a^{2}+82a+18\right){x}+911a^{3}-2655a^{2}+615a+440$ |
*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.
