| 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 |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.57742$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$10.73961278$ |
0.471725361 |
\( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 3 a\) , \( a + 1\) , \( -16 a^{3} + 36 a^{2} + 39 a - 49\) , \( -57 a^{3} + 134 a^{2} + 126 a - 168\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a\right){x}^{2}+\left(-16a^{3}+36a^{2}+39a-49\right){x}-57a^{3}+134a^{2}+126a-168$ |
| 1.1-a2 |
1.1-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.57742$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$869.9086354$ |
0.471725361 |
\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 3 a\) , \( a + 1\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( -a - 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a\right){x}^{2}+\left(-a^{3}+a^{2}+4a+1\right){x}-a-1$ |
| 1.1-a3 |
1.1-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.57742$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$10.73961278$ |
0.471725361 |
\( 3292211757861632 a^{3} - 7770967386451264 a^{2} - 7075906078720256 a + 9134646147509504 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a + 1\) , \( a\) , \( -5 a^{2} - 4 a - 4\) , \( -4 a^{3} - 17 a^{2} - 10 a - 6\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a^{2}-4a-4\right){x}-4a^{3}-17a^{2}-10a-6$ |
| 1.1-a4 |
1.1-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.57742$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$869.9086354$ |
0.471725361 |
\( 67584 a^{3} - 160832 a^{2} - 143360 a + 192256 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a + 1\) , \( a\) , \( a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}$ |
| 4.1-a1 |
4.1-a |
$2$ |
$5$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{70} \) |
$5.44350$ |
$(a^3-2a^2-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$1.502107133$ |
0.733092880 |
\( \frac{316244205973}{262144} a^{3} - \frac{316244205973}{131072} a^{2} - \frac{316244205973}{131072} a - \frac{130546611581}{262144} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{2} + a + 2\) , \( a^{3} - a^{2} - 3 a\) , \( 869 a^{3} - 2045 a^{2} - 1866 a + 2399\) , \( -1631 a^{3} + 3851 a^{2} + 3494 a - 4545\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(869a^{3}-2045a^{2}-1866a+2399\right){x}-1631a^{3}+3851a^{2}+3494a-4545$ |
| 4.1-a2 |
4.1-a |
$2$ |
$5$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{14} \) |
$5.44350$ |
$(a^3-2a^2-2a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$938.8169583$ |
0.733092880 |
\( -\frac{22614787}{16} a^{3} + \frac{22614787}{8} a^{2} + \frac{22614787}{8} a - \frac{54570013}{16} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -3 a^{3} + 3 a^{2} + 5 a + 2\) , \( 3 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-3a^{3}+3a^{2}+5a+2\right){x}+3a$ |
| 16.1-a1 |
16.1-a |
$6$ |
$8$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$6.47345$ |
$(a^3-2a^2-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$3253.435303$ |
0.992385215 |
\( -810976 a^{3} + 1621952 a^{2} + 1621952 a + 340816 \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( -4 a^{3} + 9 a^{2} + 7 a - 12\) , \( 7 a^{3} - 17 a^{2} - 16 a + 19\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-1\right){x}^{2}+\left(-4a^{3}+9a^{2}+7a-12\right){x}+7a^{3}-17a^{2}-16a+19$ |
| 16.1-a2 |
16.1-a |
$6$ |
$8$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$6.47345$ |
$(a^3-2a^2-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$813.3588257$ |
0.992385215 |
\( -1122786197316 a^{3} + 1331497041288 a^{2} + 4452350886160 a + 1379150562144 \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( 16 a^{3} - 31 a^{2} - 48 a + 18\) , \( 15 a^{3} - 49 a^{2} - 13 a + 86\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-1\right){x}^{2}+\left(16a^{3}-31a^{2}-48a+18\right){x}+15a^{3}-49a^{2}-13a+86$ |
| 16.1-a3 |
16.1-a |
$6$ |
$8$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$6.47345$ |
$(a^3-2a^2-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$203.3397064$ |
0.992385215 |
\( 54722560 a^{3} - 129179680 a^{2} - 117596128 a + 151876368 \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{2} + 3 a + 1\) , \( a^{2} - a - 1\) , \( -a^{3} + 3 a^{2} + 2 a - 1\) , \( -a^{2} + a\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+3a+1\right){x}^{2}+\left(-a^{3}+3a^{2}+2a-1\right){x}-a^{2}+a$ |
| 16.1-a4 |
16.1-a |
$6$ |
$8$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$6.47345$ |
$(a^3-2a^2-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$203.3397064$ |
0.992385215 |
\( 7102432 a^{3} + 5529696 a^{2} - 6053856 a - 2567568 \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 2 a^{2} + a\) , \( a^{2} - a - 1\) , \( -a^{2} - a + 4\) , \( -5 a^{3} + 11 a^{2} + 11 a - 12\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a\right){x}^{2}+\left(-a^{2}-a+4\right){x}-5a^{3}+11a^{2}+11a-12$ |
| 16.1-a5 |
16.1-a |
$6$ |
$8$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$6.47345$ |
$(a^3-2a^2-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$813.3588257$ |
0.992385215 |
\( -744158412476 a^{3} + 2402392178296 a^{2} - 718461666576 a - 605819928208 \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - a^{2} - 3 a\) , \( 4 a^{3} - 10 a^{2} + 8 a + 1\) , \( -6 a^{3} + 47 a^{2} - 18 a - 12\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(4a^{3}-10a^{2}+8a+1\right){x}-6a^{3}+47a^{2}-18a-12$ |
| 16.1-a6 |
16.1-a |
$6$ |
$8$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$6.47345$ |
$(a^3-2a^2-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$813.3588257$ |
0.992385215 |
\( 4096 a^{3} - 8192 a^{2} - 8192 a + 12288 \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 0\) , \( -6 a^{3} + 14 a^{2} + 12 a - 13\) , \( -13 a^{3} + 31 a^{2} + 27 a - 36\bigr] \) |
${y}^2={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(-6a^{3}+14a^{2}+12a-13\right){x}-13a^{3}+31a^{2}+27a-36$ |
| 17.1-a1 |
17.1-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{9} \) |
$6.52269$ |
$(-a^3+3a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$22.84471672$ |
1.003428379 |
\( -\frac{125949909991224098384}{118587876497} a^{3} + \frac{406619156362209680285}{118587876497} a^{2} - \frac{121639124241891855960}{118587876497} a - \frac{102511725761601225751}{118587876497} \) |
\( \bigl[1\) , \( a^{2} - a\) , \( a^{2} - 2 a\) , \( 9 a^{3} - 5 a^{2} + a\) , \( 25 a^{3} - 27 a^{2} - 2 a + 3\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(a^{2}-a\right){x}^{2}+\left(9a^{3}-5a^{2}+a\right){x}+25a^{3}-27a^{2}-2a+3$ |
| 17.1-a2 |
17.1-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{18} \) |
$6.52269$ |
$(-a^3+3a^2-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$11.42235836$ |
1.003428379 |
\( -\frac{200453408476024950974202661}{14063084452067724991009} a^{3} + \frac{594760305170886076198715871}{14063084452067724991009} a^{2} - \frac{58716294436346635030848474}{14063084452067724991009} a - \frac{109575797174460277601620265}{14063084452067724991009} \) |
\( \bigl[a^{3} - 2 a^{2} - a + 2\) , \( a^{3} - 3 a^{2} + 1\) , \( 1\) , \( -2 a^{3} + 17 a^{2} - 14 a - 50\) , \( -110 a^{3} + 288 a^{2} + 190 a - 406\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a^{2}+1\right){x}^{2}+\left(-2a^{3}+17a^{2}-14a-50\right){x}-110a^{3}+288a^{2}+190a-406$ |
| 17.1-a3 |
17.1-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$6.52269$ |
$(-a^3+3a^2-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1850.422054$ |
1.003428379 |
\( \frac{12719452}{4913} a^{3} - \frac{37372005}{4913} a^{2} - \frac{37619006}{4913} a + \frac{47560280}{4913} \) |
\( \bigl[a^{3} - 2 a^{2} - a + 2\) , \( a^{3} - 3 a^{2} + 1\) , \( 1\) , \( -2 a^{3} + 7 a^{2} + a - 5\) , \( a^{3} - 2 a^{2} + 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a^{2}+1\right){x}^{2}+\left(-2a^{3}+7a^{2}+a-5\right){x}+a^{3}-2a^{2}+1$ |
| 17.1-a4 |
17.1-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{6} \) |
$6.52269$ |
$(-a^3+3a^2-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$925.2110272$ |
1.003428379 |
\( \frac{234759643179701}{24137569} a^{3} + \frac{187290279337514}{24137569} a^{2} - \frac{192015573025041}{24137569} a - \frac{82539013284949}{24137569} \) |
\( \bigl[a^{3} - 2 a^{2} - a + 2\) , \( a^{3} - 3 a^{2} + 1\) , \( 1\) , \( 3 a^{3} - 3 a^{2} - 14 a\) , \( 2 a^{3} - 9 a^{2} + 3 a + 19\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a^{2}+1\right){x}^{2}+\left(3a^{3}-3a^{2}-14a\right){x}+2a^{3}-9a^{2}+3a+19$ |
| 17.2-a1 |
17.2-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{18} \) |
$6.52269$ |
$(a^3-a^2-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$11.42235836$ |
1.003428379 |
\( -\frac{272369543426749139452835359}{14063084452067724991009} a^{3} + \frac{350885598634662104655360169}{14063084452067724991009} a^{2} + \frac{1004362198241894815884924514}{14063084452067724991009} a + \frac{328152397580599868192045986}{14063084452067724991009} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 5 a^{3} - 20 a^{2} + 6 a - 5\) , \( 3 a^{3} - 79 a^{2} + 16 a + 15\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a^{3}-20a^{2}+6a-5\right){x}+3a^{3}-79a^{2}+16a+15$ |
| 17.2-a2 |
17.2-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{6} \) |
$6.52269$ |
$(a^3-a^2-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$925.2110272$ |
1.003428379 |
\( \frac{1825882487907894}{24137569} a^{3} - \frac{4308574541512704}{24137569} a^{2} - \frac{3929268689150149}{24137569} a + \frac{5070135373262185}{24137569} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 6 a - 5\) , \( a^{3} + 3 a^{2} - 7 a + 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-5\right){x}+a^{3}+3a^{2}-7a+3$ |
| 17.2-a3 |
17.2-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{3} \) |
$6.52269$ |
$(a^3-a^2-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1850.422054$ |
1.003428379 |
\( -\frac{23326852}{4913} a^{3} + \frac{58586805}{4913} a^{2} + \frac{58833806}{4913} a - \frac{60331631}{4913} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
| 17.2-a4 |
17.2-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{9} \) |
$6.52269$ |
$(a^3-a^2-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$22.84471672$ |
1.003428379 |
\( -\frac{190050181456041184078}{118587876497} a^{3} + \frac{225381026532320884639}{118587876497} a^{2} + \frac{753639307136422420884}{118587876497} a + \frac{233445740448049053412}{118587876497} \) |
\( \bigl[1\) , \( a^{3} - 3 a^{2} - a + 2\) , \( a^{2} - 2 a\) , \( 52 a^{3} - 116 a^{2} - 123 a + 123\) , \( 66 a^{3} - 144 a^{2} - 158 a + 136\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+2\right){x}^{2}+\left(52a^{3}-116a^{2}-123a+123\right){x}+66a^{3}-144a^{2}-158a+136$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{10} \) |
$6.84483$ |
$(a^3-a^2-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.003200617$ |
$896.1450129$ |
1.119850882 |
\( -\frac{2103803}{3125} a^{3} - \frac{2899776}{625} a^{2} + \frac{9810218}{3125} a + \frac{4628218}{3125} \) |
\( \bigl[a + 1\) , \( 1\) , \( a^{3} - 2 a^{2} - a + 1\) , \( -a^{3} + a^{2} + 3 a\) , \( -a^{2} + a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a^{2}-a+1\right){y}={x}^{3}+{x}^{2}+\left(-a^{3}+a^{2}+3a\right){x}-a^{2}+a+1$ |
| 25.2-a1 |
25.2-a |
$1$ |
$1$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$6.84483$ |
$(a^3-a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.003200617$ |
$896.1450129$ |
1.119850882 |
\( -\frac{33914163}{3125} a^{3} + \frac{86534812}{3125} a^{2} + \frac{62225714}{3125} a - \frac{23022392}{625} \) |
\( \bigl[a^{3} - 2 a^{2} - a + 1\) , \( a^{3} - 3 a^{2} + a + 1\) , \( a^{3} - 2 a^{2} - a + 1\) , \( -2 a^{3} + 6 a^{2} + 2 a - 5\) , \( 2 a^{3} - 5 a^{2} - a + 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-a+1\right){x}{y}+\left(a^{3}-2a^{2}-a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}+a+1\right){x}^{2}+\left(-2a^{3}+6a^{2}+2a-5\right){x}+2a^{3}-5a^{2}-a+3$ |
| 28.1-a1 |
28.1-a |
$1$ |
$1$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{11} \) |
$6.94249$ |
$(-a^3+3a^2+a-3), (a^3-2a^2-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$56.82972300$ |
1.109413953 |
\( -\frac{431515410343}{1977326743} a^{3} + \frac{343844253719}{3954653486} a^{2} + \frac{638287309115}{564950498} a + \frac{3374235138465}{3954653486} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{2} - a\) , \( -a^{3} + 4 a + 4\) , \( -a^{3} + 5 a\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-a^{3}+4a+4\right){x}-a^{3}+5a$ |
| 28.1-b1 |
28.1-b |
$3$ |
$9$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{3} \) |
$6.94249$ |
$(-a^3+3a^2+a-3), (a^3-2a^2-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 3^{2} \) |
$1$ |
$0.086200003$ |
1.226741051 |
\( \frac{30605504288817564444874727493}{1372} a^{3} - \frac{9073654764025227780313344097}{343} a^{2} - \frac{8668892434706707738766984651}{98} a - \frac{37593604481230384734448834573}{1372} \) |
\( \bigl[a^{2} - 2 a\) , \( -a^{2} + 2 a + 1\) , \( 1\) , \( 110 a^{3} - 6 a^{2} - 658 a - 729\) , \( 2316 a^{3} - 1466 a^{2} - 11382 a - 8128\bigr] \) |
${y}^2+\left(a^{2}-2a\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(110a^{3}-6a^{2}-658a-729\right){x}+2316a^{3}-1466a^{2}-11382a-8128$ |
| 28.1-b2 |
28.1-b |
$3$ |
$9$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{9} \) |
$6.94249$ |
$(-a^3+3a^2+a-3), (a^3-2a^2-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$6.982200318$ |
1.226741051 |
\( \frac{129496346310359743}{1291315424} a^{3} - \frac{76783377063240697}{645657712} a^{2} - \frac{18339751197705607}{46118408} a - \frac{159066160273707237}{1291315424} \) |
\( \bigl[a^{2} - 2 a\) , \( -a^{2} + 2 a + 1\) , \( 1\) , \( 4 a^{2} - 8 a - 9\) , \( 4 a^{3} - 2 a^{2} - 22 a - 16\bigr] \) |
${y}^2+\left(a^{2}-2a\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(4a^{2}-8a-9\right){x}+4a^{3}-2a^{2}-22a-16$ |
| 28.1-b3 |
28.1-b |
$3$ |
$9$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{3} \) |
$6.94249$ |
$(-a^3+3a^2+a-3), (a^3-2a^2-2a+1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$565.5582257$ |
1.226741051 |
\( \frac{1702647}{1372} a^{3} - \frac{5093723}{1372} a^{2} + \frac{53419}{196} a + \frac{902449}{686} \) |
\( \bigl[a^{2} - 2 a\) , \( -a^{2} + 2 a + 1\) , \( 1\) , \( -a^{2} + 2 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-2a\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(-a^{2}+2a+1\right){x}$ |
| 28.2-a1 |
28.2-a |
$1$ |
$1$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{11} \) |
$6.94249$ |
$(-a^2+a+2), (a^3-2a^2-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$56.82972300$ |
1.109413953 |
\( -\frac{885516073559}{3954653486} a^{3} + \frac{450464219253}{564950498} a^{2} - \frac{970917375315}{3954653486} a - \frac{408693765120}{1977326743} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{3} + 3 a^{2} - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -2 a^{3} + 5 a^{2} + a - 3\) , \( -a^{3} + 2 a^{2} - a - 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}-2\right){x}^{2}+\left(-2a^{3}+5a^{2}+a-3\right){x}-a^{3}+2a^{2}-a-3$ |
| 28.2-b1 |
28.2-b |
$3$ |
$9$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{3} \) |
$6.94249$ |
$(-a^2+a+2), (a^3-2a^2-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 3^{2} \) |
$1$ |
$0.086200003$ |
1.226741051 |
\( \frac{20284797823627220528878554561}{1372} a^{3} - \frac{2338785184599594958080470990}{49} a^{2} + \frac{9791944930502169197615610503}{686} a + \frac{16514151152991580739047055357}{1372} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( 0\) , \( 1\) , \( 100 a^{3} - 415 a^{2} + 240 a - 105\) , \( 1898 a^{3} - 6962 a^{2} + 2954 a + 534\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+{y}={x}^{3}+\left(100a^{3}-415a^{2}+240a-105\right){x}+1898a^{3}-6962a^{2}+2954a+534$ |
| 28.2-b2 |
28.2-b |
$3$ |
$9$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{3} \) |
$6.94249$ |
$(-a^2+a+2), (a^3-2a^2-2a+1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$565.5582257$ |
1.226741051 |
\( \frac{526254}{343} a^{3} - \frac{360229}{196} a^{2} - \frac{7989259}{1372} a - \frac{2455651}{1372} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+{y}={x}^{3}$ |
| 28.2-b3 |
28.2-b |
$3$ |
$9$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{9} \) |
$6.94249$ |
$(-a^2+a+2), (a^3-2a^2-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$6.982200318$ |
1.226741051 |
\( \frac{85827882383798417}{1291315424} a^{3} - \frac{19791550232988209}{92236816} a^{2} + \frac{20716144036860169}{322828856} a + \frac{69874727355884387}{1291315424} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( 0\) , \( 1\) , \( -5 a^{2} + 10 a + 5\) , \( 2 a^{3} - 10 a^{2} + 10 a - 2\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+{y}={x}^{3}+\left(-5a^{2}+10a+5\right){x}+2a^{3}-10a^{2}+10a-2$ |
| 41.1-a1 |
41.1-a |
$2$ |
$2$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$7.28146$ |
$(-a^3+2a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$174.3911381$ |
1.702207505 |
\( \frac{50004352}{1681} a^{3} + \frac{1743936}{1681} a^{2} - \frac{344715264}{1681} a - \frac{122105280}{1681} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{2} - a - 1\) , \( a^{2} - 2 a\) , \( a^{3} - 3 a^{2} + 1\) , \( -a^{3} - 2 a^{2} + 2 a\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(a^{3}-3a^{2}+1\right){x}-a^{3}-2a^{2}+2a$ |
| 41.1-a2 |
41.1-a |
$2$ |
$2$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$7.28146$ |
$(-a^3+2a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$174.3911381$ |
1.702207505 |
\( -\frac{435821039872}{41} a^{3} + \frac{516833403584}{41} a^{2} + \frac{1728225684224}{41} a + \frac{535332600576}{41} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a - 1\) , \( a\) , \( 2 a^{2} + a - 2\) , \( a^{2} - 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a^{2}+a-2\right){x}+a^{2}-1$ |
| 41.1-b1 |
41.1-b |
$2$ |
$2$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$7.28146$ |
$(-a^3+2a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$174.3911381$ |
1.702207505 |
\( \frac{8803072}{1681} a^{3} - \frac{119358784}{1681} a^{2} + \frac{227100416}{1681} a + \frac{100750080}{1681} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 3 a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - a + 1\) , \( -6 a^{3} + 16 a^{2} + 6 a - 17\) , \( -a^{3} + 2 a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-2a^{2}-a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}-a-2\right){x}^{2}+\left(-6a^{3}+16a^{2}+6a-17\right){x}-a^{3}+2a^{2}+a+1$ |
| 41.1-b2 |
41.1-b |
$2$ |
$2$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$7.28146$ |
$(-a^3+2a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$174.3911381$ |
1.702207505 |
\( -\frac{288854787712}{41} a^{3} + \frac{932518251584}{41} a^{2} - \frac{278874029056}{41} a - \frac{235160923584}{41} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 5 a^{3} - 13 a^{2} - 10 a + 15\) , \( 2 a^{3} - 6 a^{2} - 4 a + 7\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+1\right){x}^{2}+\left(5a^{3}-13a^{2}-10a+15\right){x}+2a^{3}-6a^{2}-4a+7$ |
| 49.1-a1 |
49.1-a |
$2$ |
$2$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.44552$ |
$(-a^3+3a^2+a-3), (-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.007510917$ |
$1331.429247$ |
1.561777484 |
\( -\frac{13298986880}{2401} a^{3} + \frac{42933262144}{2401} a^{2} - \frac{1833696512}{343} a - \frac{10829641152}{2401} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{3} - 2 a^{2} - 2 a\) , \( a + 1\) , \( -2 a^{2} + 5 a\) , \( -2 a^{3} + 7 a^{2} - 4 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a\right){x}^{2}+\left(-2a^{2}+5a\right){x}-2a^{3}+7a^{2}-4a-1$ |
| 49.1-a2 |
49.1-a |
$2$ |
$2$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.44552$ |
$(-a^3+3a^2+a-3), (-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.015021835$ |
$1331.429247$ |
1.561777484 |
\( \frac{4162437632}{2401} a^{3} - \frac{1405997248}{343} a^{2} - \frac{8915984128}{2401} a + \frac{11598592000}{2401} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{3} - 3 a^{2} - a + 2\) , \( a^{3} - 2 a^{2} - a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 4 a^{2} - a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-2a^{2}-a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+2\right){x}^{2}+\left(a^{3}-2a^{2}-2a+1\right){x}-a^{3}+4a^{2}-a-1$ |
| 49.1-b1 |
49.1-b |
$2$ |
$2$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.44552$ |
$(-a^3+3a^2+a-3), (-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.015021835$ |
$1331.429247$ |
1.561777484 |
\( \frac{537117824}{2401} a^{3} + \frac{442869824}{2401} a^{2} - \frac{69018112}{343} a - \frac{203364032}{2401} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - 2 a^{2} - a\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 4 a^{3} - 5 a^{2} - 11 a + 5\) , \( 2 a^{3} - 2 a^{2} + 6\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a\right){x}^{2}+\left(4a^{3}-5a^{2}-11a+5\right){x}+2a^{3}-2a^{2}+6$ |
| 49.1-b2 |
49.1-b |
$2$ |
$2$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.44552$ |
$(-a^3+3a^2+a-3), (-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.007510917$ |
$1331.429247$ |
1.561777484 |
\( -\frac{20062259456}{2401} a^{3} + \frac{3398461504}{343} a^{2} + \frac{79558368256}{2401} a + \frac{24649678848}{2401} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + a^{2} + 4 a\) , \( a\) , \( -a\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}-a{x}$ |
| 49.2-a1 |
49.2-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{2} \) |
$7.44552$ |
$(2a^3-4a^2-4a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$2.224783923$ |
$4.195558565$ |
1.639978745 |
\( -\frac{3349518877107835028}{7} a^{3} + \frac{3972146887851367633}{7} a^{2} + 1897476380986250154 a + \frac{4114307012686896152}{7} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{2} - a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 3 a^{3} - 31 a^{2} + 94 a - 76\) , \( 93 a^{3} - 413 a^{2} + 514 a - 228\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(3a^{3}-31a^{2}+94a-76\right){x}+93a^{3}-413a^{2}+514a-228$ |
| 49.2-a2 |
49.2-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.44552$ |
$(2a^3-4a^2-4a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.741594641$ |
$339.8402438$ |
1.639978745 |
\( -\frac{95945816}{343} a^{3} + \frac{114547151}{343} a^{2} + \frac{378389936}{343} a + \frac{16791237}{49} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{2} - a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 3 a^{3} - 6 a^{2} - 6 a + 4\) , \( 2 a - 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(3a^{3}-6a^{2}-6a+4\right){x}+2a-3$ |
| 49.2-a3 |
49.2-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{12} \) |
$7.44552$ |
$(2a^3-4a^2-4a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.483189282$ |
$84.96006096$ |
1.639978745 |
\( -\frac{1376412886859}{117649} a^{3} + \frac{4467102384119}{117649} a^{2} - \frac{1339803543216}{117649} a - \frac{1127343506775}{117649} \) |
\( \bigl[a^{2} - 2 a\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{3} - 2 a^{2} - 2 a + 1\) , \( 24 a^{3} - 25 a^{2} - 102 a - 39\) , \( 248 a^{3} - 296 a^{2} - 980 a - 300\bigr] \) |
${y}^2+\left(a^{2}-2a\right){x}{y}+\left(a^{3}-2a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(24a^{3}-25a^{2}-102a-39\right){x}+248a^{3}-296a^{2}-980a-300$ |
| 49.2-a4 |
49.2-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{4} \) |
$7.44552$ |
$(2a^3-4a^2-4a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$4.449567846$ |
$1.048889641$ |
1.639978745 |
\( -\frac{4002298107394794179275087}{49} a^{3} + \frac{12920731908732474125227032}{49} a^{2} - \frac{3864005251993806313800823}{49} a - \frac{3258329537199756643860265}{49} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( 1238 a^{3} - 1586 a^{2} - 4693 a - 1437\) , \( 36813 a^{3} - 44471 a^{2} - 144333 a - 44533\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(1238a^{3}-1586a^{2}-4693a-1437\right){x}+36813a^{3}-44471a^{2}-144333a-44533$ |
| 49.2-b1 |
49.2-b |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{12} \) |
$7.44552$ |
$(2a^3-4a^2-4a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.483189282$ |
$84.96006096$ |
1.639978745 |
\( -\frac{2040488982991}{117649} a^{3} + \frac{2366701355581}{117649} a^{2} + \frac{8173607282916}{117649} a + \frac{2687334132164}{117649} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( -a^{2} + a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 1\) , \( 17 a^{3} - 56 a^{2} + 17 a + 14\) , \( 164 a^{3} - 528 a^{2} + 156 a + 132\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{3}-2a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(17a^{3}-56a^{2}+17a+14\right){x}+164a^{3}-528a^{2}+156a+132$ |
| 49.2-b2 |
49.2-b |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{2} \) |
$7.44552$ |
$(2a^3-4a^2-4a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$2.224783923$ |
$4.195558565$ |
1.639978745 |
\( -\frac{2220003697148358852}{7} a^{3} + \frac{7166898260661020127}{7} a^{2} - \frac{2143289518391363318}{7} a - 258190746641008395 \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 3 a^{2} + a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( 50 a^{3} - 72 a^{2} - 205 a - 58\) , \( 314 a^{3} - 425 a^{2} - 1331 a - 414\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-3a^{2}+a+1\right){x}^{2}+\left(50a^{3}-72a^{2}-205a-58\right){x}+314a^{3}-425a^{2}-1331a-414$ |
| 49.2-b3 |
49.2-b |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.44552$ |
$(2a^3-4a^2-4a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.741594641$ |
$339.8402438$ |
1.639978745 |
\( -\frac{64136474}{343} a^{3} + \frac{205617429}{343} a^{2} - \frac{8317908}{49} a - \frac{50876100}{343} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 3 a^{2} + a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( 3 a^{2} - 5 a - 3\) , \( 2 a^{3} - 3 a^{2} - 4 a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-3a^{2}+a+1\right){x}^{2}+\left(3a^{2}-5a-3\right){x}+2a^{3}-3a^{2}-4a-1$ |
| 49.2-b4 |
49.2-b |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{4} \) |
$7.44552$ |
$(2a^3-4a^2-4a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$4.449567846$ |
$1.048889641$ |
1.639978745 |
\( -\frac{6038628186292417318272368}{49} a^{3} + \frac{7161120678641948869867878}{49} a^{2} + \frac{23945857839368229308895733}{49} a + \frac{7417417386833654378175747}{49} \) |
\( \bigl[1\) , \( a^{2} - 3 a - 1\) , \( a^{2} - 2 a - 1\) , \( -2299 a^{3} + 5370 a^{2} + 4993 a - 6391\) , \( -63455 a^{3} + 149408 a^{2} + 136750 a - 176122\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(a^{2}-3a-1\right){x}^{2}+\left(-2299a^{3}+5370a^{2}+4993a-6391\right){x}-63455a^{3}+149408a^{2}+136750a-176122$ |
| 49.3-a1 |
49.3-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.44552$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.115090895$ |
$312.5508098$ |
1.404460983 |
\( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \) |
\( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 15 a^{3} - 62 a^{2} + 53 a - 13\) , \( -93 a^{3} + 335 a^{2} - 211 a - 6\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(15a^{3}-62a^{2}+53a-13\right){x}-93a^{3}+335a^{2}-211a-6$ |
| 49.3-a2 |
49.3-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.44552$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.038363631$ |
$937.6524294$ |
1.404460983 |
\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \) |
\( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 2 a^{2} - a + 2\) , \( -2 a^{2} + 3 a + 2\) , \( 2 a^{3} - 7 a^{2} + 2 a + 1\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-2a^{2}+3a+2\right){x}+2a^{3}-7a^{2}+2a+1$ |
| 49.3-a3 |
49.3-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.44552$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.057545447$ |
$312.5508098$ |
1.404460983 |
\( 3292211757861632 a^{3} - 7770967386451264 a^{2} - 7075906078720256 a + 9134646147509504 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a\) , \( a^{2} - 2 a - 1\) , \( -41 a^{3} + 99 a^{2} + 93 a - 148\) , \( 232 a^{3} - 512 a^{2} - 596 a + 646\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}-a{x}^{2}+\left(-41a^{3}+99a^{2}+93a-148\right){x}+232a^{3}-512a^{2}-596a+646$ |
| 49.3-a4 |
49.3-a |
$4$ |
$6$ |
4.4.2624.1 |
$4$ |
$[4, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{6} \) |
$7.44552$ |
$(-a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.019181815$ |
$937.6524294$ |
1.404460983 |
\( 67584 a^{3} - 160832 a^{2} - 143360 a + 192256 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a\) , \( a^{2} - 2 a - 1\) , \( -a^{3} + 4 a^{2} - 2 a - 3\) , \( a^{3} - 3 a^{2} + 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}-a{x}^{2}+\left(-a^{3}+4a^{2}-2a-3\right){x}+a^{3}-3a^{2}+1$ |
*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.
