| 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 |
| 4.1-a1 |
4.1-a |
$2$ |
$5$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$3225.401661$ |
1.56133382 |
\( \frac{218959}{32} a^{4} - \frac{201429}{16} a^{3} - \frac{960485}{32} a^{2} + \frac{749777}{32} a + \frac{136963}{16} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + a + 4\) , \( -a^{4} + a^{3} + 7 a^{2} - a - 6\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 5 a - 2\) , \( 3 a^{4} - 5 a^{3} - 14 a^{2} + 9 a + 6\) , \( -2 a^{4} + 4 a^{3} + 9 a^{2} - 10 a - 4\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+a+4\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-5a-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+7a^{2}-a-6\right){x}^{2}+\left(3a^{4}-5a^{3}-14a^{2}+9a+6\right){x}-2a^{4}+4a^{3}+9a^{2}-10a-4$ |
| 4.1-a2 |
4.1-a |
$2$ |
$5$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$1.032128531$ |
1.56133382 |
\( 3656022473178131251 a^{4} - \frac{20255803144684800007}{2} a^{3} - 4007790797515828126 a^{2} + \frac{14189147585771506271}{2} a + \frac{4130647227075007735}{2} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + 4 a + 7\) , \( a^{4} - a^{3} - 6 a^{2} + 3\) , \( 28 a^{4} + 152 a^{3} - 244 a^{2} - 1061 a - 545\) , \( 1869 a^{4} + 193 a^{3} - 11016 a^{2} - 13031 a - 5830\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+3\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-11a^{2}+4a+7\right){x}^{2}+\left(28a^{4}+152a^{3}-244a^{2}-1061a-545\right){x}+1869a^{4}+193a^{3}-11016a^{2}-13031a-5830$ |
| 4.1-b1 |
4.1-b |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{16} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1640.778721$ |
1.98564674 |
\( -\frac{454623215}{256} a^{4} + \frac{99823045}{32} a^{3} + \frac{2124079509}{256} a^{2} - \frac{1608918299}{256} a - \frac{37525927}{16} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( a^{4} - a^{3} - 5 a^{2} - a + 1\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 5 a - 3\) , \( a^{4} - a^{3} - 5 a^{2} - a\) , \( -3 a^{4} + 4 a^{3} + 17 a^{2} - 6 a - 12\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-5a-3\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}-a+1\right){x}^{2}+\left(a^{4}-a^{3}-5a^{2}-a\right){x}-3a^{4}+4a^{3}+17a^{2}-6a-12$ |
| 4.1-b2 |
4.1-b |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$3281.557443$ |
1.98564674 |
\( -17721 a^{4} + \frac{1885}{2} a^{3} + 107709 a^{2} + \frac{205165}{2} a + \frac{44295}{2} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + a + 4\) , \( a^{4} - a^{3} - 5 a^{2} - 2 a\) , \( a^{4} - a^{3} - 6 a^{2} + a + 4\) , \( -2 a^{4} + a^{3} + 12 a^{2} + 5 a - 2\) , \( a^{3} - a^{2} - 5 a - 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+a+4\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+a+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}-2a\right){x}^{2}+\left(-2a^{4}+a^{3}+12a^{2}+5a-2\right){x}+a^{3}-a^{2}-5a-3$ |
| 4.1-b3 |
4.1-b |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$6563.114886$ |
1.98564674 |
\( \frac{655897}{4} a^{4} - 463134 a^{3} - \frac{592671}{4} a^{2} + \frac{1216057}{4} a + 87721 \) |
\( \bigl[a + 1\) , \( -2 a^{4} + 3 a^{3} + 10 a^{2} - 3 a - 5\) , \( -2 a^{4} + 4 a^{3} + 9 a^{2} - 9 a - 4\) , \( 2 a^{4} - 3 a^{3} - 9 a^{2} + 4 a + 5\) , \( 3 a^{4} - 4 a^{3} - 15 a^{2} + 6 a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-2a^{4}+4a^{3}+9a^{2}-9a-4\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+10a^{2}-3a-5\right){x}^{2}+\left(2a^{4}-3a^{3}-9a^{2}+4a+5\right){x}+3a^{4}-4a^{3}-15a^{2}+6a+2$ |
| 4.1-b4 |
4.1-b |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$3281.557443$ |
1.98564674 |
\( \frac{603355}{4} a^{4} - \frac{3848237}{16} a^{3} - \frac{3327539}{4} a^{2} + \frac{8411131}{16} a + \frac{11595855}{16} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 4 a\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( -4 a^{4} + 9 a^{3} + 7 a^{2} + 3 a - 5\) , \( -9 a^{4} + 23 a^{3} + 14 a^{2} - 12 a - 9\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-4a\right){x}{y}+\left(a^{3}-2a^{2}-4a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-4a^{4}+9a^{3}+7a^{2}+3a-5\right){x}-9a^{4}+23a^{3}+14a^{2}-12a-9$ |
| 4.1-b5 |
4.1-b |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$820.3893608$ |
1.98564674 |
\( 563906871306 a^{4} - \frac{3124767358987}{2} a^{3} - 617274409019 a^{2} + \frac{2187744509897}{2} a + \frac{636737160719}{2} \) |
\( \bigl[a + 1\) , \( -2 a^{4} + 3 a^{3} + 10 a^{2} - 3 a - 5\) , \( -2 a^{4} + 4 a^{3} + 9 a^{2} - 9 a - 4\) , \( 2 a^{4} - 8 a^{3} - 4 a^{2} + 29 a + 5\) , \( 16 a^{4} - 27 a^{3} - 79 a^{2} + 55 a + 35\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-2a^{4}+4a^{3}+9a^{2}-9a-4\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+10a^{2}-3a-5\right){x}^{2}+\left(2a^{4}-8a^{3}-4a^{2}+29a+5\right){x}+16a^{4}-27a^{3}-79a^{2}+55a+35$ |
| 4.1-b6 |
4.1-b |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$102.5486701$ |
1.98564674 |
\( \frac{326580830299}{4} a^{4} - 125354180644 a^{3} - \frac{1811160236513}{4} a^{2} + \frac{1014250602843}{4} a + 370660279073 \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 4 a\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( -4 a^{4} - 16 a^{3} + 82 a^{2} + 8 a - 55\) , \( -99 a^{4} + 210 a^{3} + 302 a^{2} - 174 a - 186\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-4a\right){x}{y}+\left(a^{3}-2a^{2}-4a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-4a^{4}-16a^{3}+82a^{2}+8a-55\right){x}-99a^{4}+210a^{3}+302a^{2}-174a-186$ |
| 4.1-c1 |
4.1-c |
$1$ |
$1$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.100686064$ |
$1781.725747$ |
2.17101184 |
\( \frac{2069655}{2} a^{4} - 1881979 a^{3} - \frac{9638371}{2} a^{2} + \frac{7387103}{2} a + 1372350 \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 6 a\) , \( a^{4} - a^{3} - 6 a^{2} + a + 3\) , \( 17 a^{4} - 32 a^{3} - 77 a^{2} + 68 a + 25\) , \( 93 a^{4} - 163 a^{3} - 433 a^{2} + 324 a + 120\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-3a-1\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a\right){x}^{2}+\left(17a^{4}-32a^{3}-77a^{2}+68a+25\right){x}+93a^{4}-163a^{3}-433a^{2}+324a+120$ |
| 4.1-d1 |
4.1-d |
$2$ |
$2$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2867.066559$ |
1.73484130 |
\( -77442026 a^{4} + \frac{272243353}{2} a^{3} + 361508491 a^{2} - \frac{547845579}{2} a - \frac{204410793}{2} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( 2 a^{4} - 3 a^{3} - 10 a^{2} + 3 a + 4\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 5 a - 2\) , \( 25 a^{4} - 42 a^{3} - 119 a^{2} + 77 a + 35\) , \( 72 a^{4} - 126 a^{3} - 337 a^{2} + 251 a + 96\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-5a-2\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-10a^{2}+3a+4\right){x}^{2}+\left(25a^{4}-42a^{3}-119a^{2}+77a+35\right){x}+72a^{4}-126a^{3}-337a^{2}+251a+96$ |
| 4.1-d2 |
4.1-d |
$2$ |
$2$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{4} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1433.533279$ |
1.73484130 |
\( \frac{61744157}{4} a^{4} - 19597126 a^{3} - \frac{346980743}{4} a^{2} + \frac{97311829}{4} a + 54611627 \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + a + 4\) , \( a^{4} - a^{3} - 6 a^{2} + 3\) , \( -2 a^{4} + 4 a^{3} + 9 a^{2} - 8 a - 4\) , \( 2 a^{4} - 4 a^{3} - 9 a^{2} + 6 a + 6\) , \( -4 a^{4} + 5 a^{3} + 22 a^{2} - 4 a - 18\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+a+4\right){x}{y}+\left(-2a^{4}+4a^{3}+9a^{2}-8a-4\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+3\right){x}^{2}+\left(2a^{4}-4a^{3}-9a^{2}+6a+6\right){x}-4a^{4}+5a^{3}+22a^{2}-4a-18$ |
| 4.1-e1 |
4.1-e |
$2$ |
$2$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.040688280$ |
$7345.516967$ |
1.80847987 |
\( -\frac{40567231}{16} a^{4} + \frac{8913147}{2} a^{3} + \frac{189377157}{16} a^{2} - \frac{143495355}{16} a - 3346105 \) |
\( \bigl[-a^{4} + 3 a^{3} + 3 a^{2} - 9 a\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + 4 a + 5\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -3 a^{4} + 7 a^{3} + 12 a^{2} - 16 a\) , \( -5 a^{4} + 9 a^{3} + 21 a^{2} - 21 a - 4\bigr] \) |
${y}^2+\left(-a^{4}+3a^{3}+3a^{2}-9a\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-11a^{2}+4a+5\right){x}^{2}+\left(-3a^{4}+7a^{3}+12a^{2}-16a\right){x}-5a^{4}+9a^{3}+21a^{2}-21a-4$ |
| 4.1-e2 |
4.1-e |
$2$ |
$2$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$42.40944$ |
$(a^4-a^3-6a^2+a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.020344140$ |
$14691.03393$ |
1.80847987 |
\( 18974 a^{4} - \frac{103175}{4} a^{3} - 105268 a^{2} + \frac{152949}{4} a + \frac{279521}{4} \) |
\( \bigl[1\) , \( a^{2} - 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{4} - 2 a^{3} - a^{2} + 2 a - 1\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 2 a\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(a^{4}-2a^{3}-a^{2}+2a-1\right){x}+2a^{4}-3a^{3}-7a^{2}+2a$ |
| 7.1-a1 |
7.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$44.85041$ |
$(a^4-a^3-6a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$2.637519444$ |
$7.988037780$ |
2.03975374 |
\( \frac{1088882693924179124}{49} a^{4} + \frac{2078688237971056291}{49} a^{3} - \frac{74142963323223139}{7} a^{2} - \frac{228778272978719691}{7} a - \frac{370079573359621021}{49} \) |
\( \bigl[a\) , \( -2 a^{4} + 3 a^{3} + 10 a^{2} - 5 a - 5\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a\) , \( -25 a^{4} + 43 a^{3} + 89 a^{2} - 56 a - 63\) , \( -390 a^{4} + 543 a^{3} + 1950 a^{2} - 635 a - 1240\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-4a\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+10a^{2}-5a-5\right){x}^{2}+\left(-25a^{4}+43a^{3}+89a^{2}-56a-63\right){x}-390a^{4}+543a^{3}+1950a^{2}-635a-1240$ |
| 7.1-a2 |
7.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$44.85041$ |
$(a^4-a^3-6a^2+a+2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.318759722$ |
$8179.750687$ |
2.03975374 |
\( -\frac{117376319222}{7} a^{4} + \frac{206317323768}{7} a^{3} + 78274647803 a^{2} - 59312011261 a - \frac{154902648352}{7} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 5 a^{4} - 8 a^{3} - 22 a^{2} + 16 a + 5\) , \( -4 a^{4} + 8 a^{3} + 19 a^{2} - 14 a - 7\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a^{4}-8a^{3}-22a^{2}+16a+5\right){x}-4a^{4}+8a^{3}+19a^{2}-14a-7$ |
| 7.1-a3 |
7.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$44.85041$ |
$(a^4-a^3-6a^2+a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.659379861$ |
$8179.750687$ |
2.03975374 |
\( -\frac{3618627}{49} a^{4} + \frac{6313294}{49} a^{3} + \frac{2463435}{7} a^{2} - \frac{1823840}{7} a - \frac{4707380}{49} \) |
\( \bigl[a\) , \( -2 a^{4} + 3 a^{3} + 10 a^{2} - 5 a - 5\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a\) , \( -5 a^{4} + 8 a^{3} + 24 a^{2} - 11 a - 13\) , \( 5 a^{4} - 6 a^{3} - 30 a^{2} + 10 a + 17\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-4a\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+10a^{2}-5a-5\right){x}^{2}+\left(-5a^{4}+8a^{3}+24a^{2}-11a-13\right){x}+5a^{4}-6a^{3}-30a^{2}+10a+17$ |
| 7.1-a4 |
7.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$44.85041$ |
$(a^4-a^3-6a^2+a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.329689930$ |
$8179.750687$ |
2.03975374 |
\( \frac{1430388}{7} a^{4} - \frac{1834927}{7} a^{3} - 1151579 a^{2} + 324579 a + \frac{5079785}{7} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a\) , \( a^{4} - a^{3} - 6 a^{2} + a + 3\) , \( -3 a^{4} + 5 a^{3} + 14 a^{2} - 9 a - 4\) , \( -7 a^{4} + 12 a^{3} + 33 a^{2} - 23 a - 10\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a\right){x}^{2}+\left(-3a^{4}+5a^{3}+14a^{2}-9a-4\right){x}-7a^{4}+12a^{3}+33a^{2}-23a-10$ |
| 7.1-a5 |
7.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$44.85041$ |
$(a^4-a^3-6a^2+a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1.318759722$ |
$255.6172089$ |
2.03975374 |
\( \frac{120194765804}{2401} a^{4} - \frac{196452902586}{2401} a^{3} - \frac{9241520007}{343} a^{2} + \frac{26486716555}{343} a + \frac{52541477510}{2401} \) |
\( \bigl[a\) , \( -2 a^{4} + 3 a^{3} + 10 a^{2} - 5 a - 5\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a\) , \( -50 a^{4} + 78 a^{3} + 239 a^{2} - 86 a - 148\) , \( -168 a^{4} + 280 a^{3} + 748 a^{2} - 280 a - 468\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-4a\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+10a^{2}-5a-5\right){x}^{2}+\left(-50a^{4}+78a^{3}+239a^{2}-86a-148\right){x}-168a^{4}+280a^{3}+748a^{2}-280a-468$ |
| 7.1-a6 |
7.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{8} \) |
$44.85041$ |
$(a^4-a^3-6a^2+a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$2.637519444$ |
$7.988037780$ |
2.03975374 |
\( \frac{170006175375651883274764}{5764801} a^{4} - \frac{470950136165714590208851}{5764801} a^{3} - \frac{26623385358212393396973}{823543} a^{2} + \frac{47128515383273996340987}{823543} a + \frac{96038273080606136523965}{5764801} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 5 a - 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -121 a^{4} + 234 a^{3} + 588 a^{2} - 590 a - 401\) , \( -209 a^{4} + 607 a^{3} + 987 a^{2} - 2287 a - 1722\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-5a-4\right){x}^{2}+\left(-121a^{4}+234a^{3}+588a^{2}-590a-401\right){x}-209a^{4}+607a^{3}+987a^{2}-2287a-1722$ |
| 11.1-a1 |
11.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$46.92409$ |
$(-2a^4+3a^3+10a^2-4a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$4.173625715$ |
$41.15096488$ |
2.07847830 |
\( \frac{673427914790571108667402907637}{11} a^{4} + \frac{1275458418994808416445744312498}{11} a^{3} - \frac{349417437644754701169038548491}{11} a^{2} - \frac{1011206773666255520468670597552}{11} a - \frac{232699644180027797312282800956}{11} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 1\) , \( 1\) , \( -2 a^{4} + 47 a^{3} - 212 a^{2} + 241 a + 82\) , \( -378 a^{4} + 739 a^{3} + 1643 a^{2} - 1589 a - 561\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-1\right){x}^{2}+\left(-2a^{4}+47a^{3}-212a^{2}+241a+82\right){x}-378a^{4}+739a^{3}+1643a^{2}-1589a-561$ |
| 11.1-a2 |
11.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$46.92409$ |
$(-2a^4+3a^3+10a^2-4a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$4.173625715$ |
$164.6038595$ |
2.07847830 |
\( -\frac{307983870228170899253}{11} a^{4} + \frac{541356301250344470302}{11} a^{3} + \frac{1437694608890735788363}{11} a^{2} - \frac{1089402135559092976000}{11} a - \frac{406449313251114639300}{11} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 5 a + 2\) , \( -a^{4} + 3 a^{3} + 3 a^{2} - 9 a - 1\) , \( 14 a^{4} - 24 a^{3} - 71 a^{2} + 49 a + 20\) , \( -41 a^{4} + 79 a^{3} + 165 a^{2} - 144 a - 52\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-3a-1\right){x}{y}+\left(-a^{4}+3a^{3}+3a^{2}-9a-1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+5a+2\right){x}^{2}+\left(14a^{4}-24a^{3}-71a^{2}+49a+20\right){x}-41a^{4}+79a^{3}+165a^{2}-144a-52$ |
| 11.1-a3 |
11.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$46.92409$ |
$(-2a^4+3a^3+10a^2-4a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.086812857$ |
$658.4154381$ |
2.07847830 |
\( \frac{2893771692566078}{121} a^{4} + \frac{5482105271743813}{121} a^{3} - \frac{1499926040614041}{121} a^{2} - \frac{4347112941202341}{121} a - \frac{1000549450320971}{121} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 4 a\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -2 a^{4} + 4 a^{3} + 9 a^{2} - 8 a - 4\) , \( 92 a^{4} - 6 a^{3} - 563 a^{2} - 512 a - 110\) , \( 858 a^{4} - 67 a^{3} - 5238 a^{2} - 4761 a - 917\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-4a\right){x}{y}+\left(-2a^{4}+4a^{3}+9a^{2}-8a-4\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(92a^{4}-6a^{3}-563a^{2}-512a-110\right){x}+858a^{4}-67a^{3}-5238a^{2}-4761a-917$ |
| 11.1-a4 |
11.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$46.92409$ |
$(-2a^4+3a^3+10a^2-4a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.043406428$ |
$1316.830876$ |
2.07847830 |
\( \frac{78730353072088}{14641} a^{4} - \frac{218059554174846}{14641} a^{3} - \frac{86321399648629}{14641} a^{2} + \frac{152751456531917}{14641} a + \frac{44483280366586}{14641} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 5 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 1\) , \( 10 a^{4} - 15 a^{3} - 53 a^{2} + 28 a + 19\) , \( -5 a^{4} + 10 a^{3} + 15 a^{2} - 7 a + 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a+2\right){x}^{2}+\left(10a^{4}-15a^{3}-53a^{2}+28a+19\right){x}-5a^{4}+10a^{3}+15a^{2}-7a+1$ |
| 11.1-a5 |
11.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$46.92409$ |
$(-2a^4+3a^3+10a^2-4a-4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.521703214$ |
$2633.661752$ |
2.07847830 |
\( \frac{35015216115655}{121} a^{4} - \frac{44877973073404}{121} a^{3} - \frac{197460866799761}{121} a^{2} + \frac{55622731229496}{121} a + \frac{124455540192842}{121} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 4 a\) , \( -a^{4} + a^{3} + 7 a^{2} - 4\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 4 a - 2\) , \( -3 a^{4} + 7 a^{3} + 13 a^{2} - 12 a - 14\) , \( 7 a^{4} - 5 a^{3} - 55 a^{2} + 16 a + 39\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-4a\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+7a^{2}-4\right){x}^{2}+\left(-3a^{4}+7a^{3}+13a^{2}-12a-14\right){x}+7a^{4}-5a^{3}-55a^{2}+16a+39$ |
| 11.1-a6 |
11.1-a |
$6$ |
$8$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{8} \) |
$46.92409$ |
$(-2a^4+3a^3+10a^2-4a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$2.086812857$ |
$41.15096488$ |
2.07847830 |
\( \frac{116997210540066984598862108936}{214358881} a^{4} - \frac{324105056814788019290613328683}{214358881} a^{3} - \frac{128254197617343736603953868289}{214358881} a^{2} + \frac{227034905546948193427011387221}{214358881} a + \frac{66092847375756424385937060205}{214358881} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 5 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 1\) , \( 5 a^{4} + 5 a^{3} - 73 a^{2} + 38 a + 24\) , \( -46 a^{4} + 179 a^{3} - 139 a^{2} + 9 a + 22\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a+2\right){x}^{2}+\left(5a^{4}+5a^{3}-73a^{2}+38a+24\right){x}-46a^{4}+179a^{3}-139a^{2}+9a+22$ |
| 23.1-a1 |
23.1-a |
$1$ |
$1$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$50.51605$ |
$(-a^2+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.356737711$ |
$852.7119755$ |
3.68131818 |
\( \frac{212603936630272}{23} a^{4} - \frac{17990283219461}{23} a^{3} - \frac{1292091586570424}{23} a^{2} - \frac{1182756388954841}{23} a - \frac{232257258453785}{23} \) |
\( \bigl[-a^{4} + 3 a^{3} + 3 a^{2} - 8 a - 1\) , \( a^{2} - a - 2\) , \( a + 1\) , \( 4 a^{4} - 5 a^{3} - 22 a^{2} + 3 a + 22\) , \( -a^{4} + a^{3} + 8 a^{2} - 6 a - 2\bigr] \) |
${y}^2+\left(-a^{4}+3a^{3}+3a^{2}-8a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(4a^{4}-5a^{3}-22a^{2}+3a+22\right){x}-a^{4}+a^{3}+8a^{2}-6a-2$ |
| 23.1-b1 |
23.1-b |
$4$ |
$4$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( 23 \) |
$50.51605$ |
$(-a^2+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.202702905$ |
$4274.947155$ |
2.62169825 |
\( -\frac{10860531789273029}{23} a^{4} + \frac{19090016333763269}{23} a^{3} + \frac{50697878164279215}{23} a^{2} - \frac{38415930160431121}{23} a - \frac{14332750080350891}{23} \) |
\( \bigl[a\) , \( a - 1\) , \( -a^{4} + 3 a^{3} + 3 a^{2} - 9 a\) , \( -4 a^{4} + 8 a^{3} + 8 a^{2} - 8 a - 3\) , \( 13 a^{4} - 28 a^{3} - 28 a^{2} + 25 a + 7\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{4}+3a^{3}+3a^{2}-9a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a^{4}+8a^{3}+8a^{2}-8a-3\right){x}+13a^{4}-28a^{3}-28a^{2}+25a+7$ |
| 23.1-b2 |
23.1-b |
$4$ |
$4$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{4} \) |
$50.51605$ |
$(-a^2+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.810811621$ |
$534.3683943$ |
2.62169825 |
\( \frac{44148334326476547455}{279841} a^{4} + \frac{83335294531293448643}{279841} a^{3} - \frac{23359669145708602669}{279841} a^{2} - \frac{66019255447735369823}{279841} a - \frac{14910542716378572773}{279841} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 4 a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 2\) , \( 1\) , \( 29 a^{4} + a^{3} - 169 a^{2} - 202 a - 58\) , \( 236 a^{4} - 187 a^{3} - 1110 a^{2} - 878 a - 184\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-4a\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-2\right){x}^{2}+\left(29a^{4}+a^{3}-169a^{2}-202a-58\right){x}+236a^{4}-187a^{3}-1110a^{2}-878a-184$ |
| 23.1-b3 |
23.1-b |
$4$ |
$4$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$50.51605$ |
$(-a^2+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.405405810$ |
$4274.947155$ |
2.62169825 |
\( -\frac{6483097853}{529} a^{4} + \frac{12804262431}{529} a^{3} + \frac{33611786696}{529} a^{2} - \frac{20970789366}{529} a - \frac{7749132061}{529} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + 3\) , \( a^{4} - 3 a^{3} - 3 a^{2} + 10 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -54 a^{4} + 86 a^{3} + 252 a^{2} - 90 a - 144\) , \( -76 a^{4} + 12 a^{3} + 684 a^{2} - 86 a - 441\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+3\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(a^{4}-3a^{3}-3a^{2}+10a+1\right){x}^{2}+\left(-54a^{4}+86a^{3}+252a^{2}-90a-144\right){x}-76a^{4}+12a^{3}+684a^{2}-86a-441$ |
| 23.1-b4 |
23.1-b |
$4$ |
$4$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
23.1 |
\( 23 \) |
\( 23 \) |
$50.51605$ |
$(-a^2+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.810811621$ |
$1068.736788$ |
2.62169825 |
\( -\frac{325108242015746}{23} a^{4} + \frac{27510258081065}{23} a^{3} + \frac{1975831826252235}{23} a^{2} + \frac{1808639376229080}{23} a + \frac{355161576308245}{23} \) |
\( \bigl[-2 a^{4} + 4 a^{3} + 9 a^{2} - 8 a - 3\) , \( a^{4} - a^{3} - 6 a^{2} + 4\) , \( a^{4} - a^{3} - 6 a^{2} + 3\) , \( 41 a^{4} - 69 a^{3} - 193 a^{2} + 133 a + 55\) , \( -111 a^{4} + 197 a^{3} + 518 a^{2} - 400 a - 149\bigr] \) |
${y}^2+\left(-2a^{4}+4a^{3}+9a^{2}-8a-3\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+4\right){x}^{2}+\left(41a^{4}-69a^{3}-193a^{2}+133a+55\right){x}-111a^{4}+197a^{3}+518a^{2}-400a-149$ |
| 23.2-a1 |
23.2-a |
$1$ |
$1$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( 23 \) |
$50.51605$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.018686210$ |
$11486.86236$ |
2.59761403 |
\( \frac{177143211}{23} a^{4} - \frac{312306656}{23} a^{3} - \frac{827992018}{23} a^{2} + \frac{627941448}{23} a + \frac{234199849}{23} \) |
\( \bigl[1\) , \( -2 a^{4} + 3 a^{3} + 10 a^{2} - 4 a - 3\) , \( -2 a^{4} + 4 a^{3} + 9 a^{2} - 8 a - 3\) , \( a^{4} + a^{3} - 7 a^{2} - 13 a - 4\) , \( 5 a^{4} - 4 a^{3} - 28 a^{2} - 9 a - 1\bigr] \) |
${y}^2+{x}{y}+\left(-2a^{4}+4a^{3}+9a^{2}-8a-3\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+10a^{2}-4a-3\right){x}^{2}+\left(a^{4}+a^{3}-7a^{2}-13a-4\right){x}+5a^{4}-4a^{3}-28a^{2}-9a-1$ |
| 23.2-b1 |
23.2-b |
$4$ |
$4$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( - 23^{4} \) |
$50.51605$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$400.7215618$ |
0.969894907 |
\( -\frac{6397446844917649308}{279841} a^{4} + \frac{11245073912608087236}{279841} a^{3} + \frac{29863798581570057148}{279841} a^{2} - \frac{22629124850264575215}{279841} a - \frac{8442723832286052583}{279841} \) |
\( \bigl[-2 a^{4} + 4 a^{3} + 9 a^{2} - 8 a - 4\) , \( -2 a^{4} + 3 a^{3} + 10 a^{2} - 5 a - 5\) , \( a^{4} - a^{3} - 6 a^{2} + 4\) , \( 41 a^{4} + 4 a^{3} - 255 a^{2} - 269 a - 56\) , \( -329 a^{4} + 26 a^{3} + 2002 a^{2} + 1839 a + 358\bigr] \) |
${y}^2+\left(-2a^{4}+4a^{3}+9a^{2}-8a-4\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+4\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+10a^{2}-5a-5\right){x}^{2}+\left(41a^{4}+4a^{3}-255a^{2}-269a-56\right){x}-329a^{4}+26a^{3}+2002a^{2}+1839a+358$ |
| 23.2-b2 |
23.2-b |
$4$ |
$4$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$50.51605$ |
$(a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$3205.772494$ |
0.969894907 |
\( -\frac{1465937560}{529} a^{4} + \frac{2572978912}{529} a^{3} + \frac{6858990393}{529} a^{2} - \frac{5196280446}{529} a - \frac{1930941015}{529} \) |
\( \bigl[-2 a^{4} + 4 a^{3} + 9 a^{2} - 8 a - 4\) , \( -2 a^{4} + 3 a^{3} + 10 a^{2} - 5 a - 5\) , \( a^{4} - a^{3} - 6 a^{2} + 4\) , \( 6 a^{4} + 9 a^{3} - 45 a^{2} - 84 a - 16\) , \( 36 a^{4} + 10 a^{3} - 229 a^{2} - 272 a - 62\bigr] \) |
${y}^2+\left(-2a^{4}+4a^{3}+9a^{2}-8a-4\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+4\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+10a^{2}-5a-5\right){x}^{2}+\left(6a^{4}+9a^{3}-45a^{2}-84a-16\right){x}+36a^{4}+10a^{3}-229a^{2}-272a-62$ |
| 23.2-b3 |
23.2-b |
$4$ |
$4$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( 23 \) |
$50.51605$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1602.886247$ |
0.969894907 |
\( \frac{135923299}{23} a^{4} + \frac{257530210}{23} a^{3} - \frac{70407338}{23} a^{2} - \frac{204233450}{23} a - \frac{47011099}{23} \) |
\( \bigl[-2 a^{4} + 4 a^{3} + 9 a^{2} - 9 a - 4\) , \( a^{3} - a^{2} - 4 a\) , \( a^{4} - a^{3} - 6 a^{2} + a + 4\) , \( -15 a^{4} + 32 a^{3} + 51 a^{2} - 45 a - 14\) , \( -14 a^{4} + 26 a^{3} + 61 a^{2} - 47 a - 20\bigr] \) |
${y}^2+\left(-2a^{4}+4a^{3}+9a^{2}-9a-4\right){x}{y}+\left(a^{4}-a^{3}-6a^{2}+a+4\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-15a^{4}+32a^{3}+51a^{2}-45a-14\right){x}-14a^{4}+26a^{3}+61a^{2}-47a-20$ |
| 23.2-b4 |
23.2-b |
$4$ |
$4$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
23.2 |
\( 23 \) |
\( 23 \) |
$50.51605$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1602.886247$ |
0.969894907 |
\( \frac{37769644680}{23} a^{4} - \frac{104904652450}{23} a^{3} - \frac{40893000544}{23} a^{2} + \frac{74062244207}{23} a + \frac{21506557395}{23} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( -2 a^{4} + 3 a^{3} + 10 a^{2} - 5 a - 5\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -3 a^{4} + 5 a^{3} + 16 a^{2} - 10 a - 11\) , \( a^{4} - a^{3} - 6 a^{2} - a + 2\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+10a^{2}-5a-5\right){x}^{2}+\left(-3a^{4}+5a^{3}+16a^{2}-10a-11\right){x}+a^{4}-a^{3}-6a^{2}-a+2$ |
| 31.1-a1 |
31.1-a |
$2$ |
$2$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$52.04665$ |
$(-a^4+2a^3+5a^2-6a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.088890002$ |
$7343.742335$ |
3.94995662 |
\( \frac{561495}{961} a^{4} - \frac{896871}{961} a^{3} - \frac{2858624}{961} a^{2} + \frac{1962276}{961} a + \frac{2721373}{961} \) |
\( \bigl[-a^{4} + 3 a^{3} + 3 a^{2} - 9 a\) , \( -a^{4} + a^{3} + 7 a^{2} - 6\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 5 a - 3\) , \( -a^{4} + 15 a^{2} - 14 a + 1\) , \( -20 a^{4} + 45 a^{3} + 60 a^{2} - 54 a - 21\bigr] \) |
${y}^2+\left(-a^{4}+3a^{3}+3a^{2}-9a\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-5a-3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+7a^{2}-6\right){x}^{2}+\left(-a^{4}+15a^{2}-14a+1\right){x}-20a^{4}+45a^{3}+60a^{2}-54a-21$ |
| 31.1-a2 |
31.1-a |
$2$ |
$2$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
31.1 |
\( 31 \) |
\( 31 \) |
$52.04665$ |
$(-a^4+2a^3+5a^2-6a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.177780005$ |
$7343.742335$ |
3.94995662 |
\( \frac{11543751}{31} a^{4} - \frac{17634487}{31} a^{3} - \frac{64000975}{31} a^{2} + \frac{35629577}{31} a + \frac{52557747}{31} \) |
\( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 4 a - 2\) , \( a^{4} - a^{3} - 5 a^{2} - a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 8 a^{4} - 3 a^{3} - 43 a^{2} - 24 a - 3\) , \( 10 a^{4} - 57 a^{2} - 51 a - 12\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+5a^{2}-4a-2\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}-a\right){x}^{2}+\left(8a^{4}-3a^{3}-43a^{2}-24a-3\right){x}+10a^{4}-57a^{2}-51a-12$ |
| 32.1-a1 |
32.1-a |
$1$ |
$1$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{30} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$164.7488546$ |
2.39252025 |
\( -\frac{36380228233653}{256} a^{4} - \frac{17225667747151}{64} a^{3} + \frac{9438779270857}{128} a^{2} + \frac{54627167281497}{256} a + \frac{6285057258237}{128} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -2 a^{4} + 3 a^{3} + 11 a^{2} - 6 a - 6\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 5 a - 3\) , \( -22 a^{4} + 17 a^{3} + 104 a^{2} - 27 a - 59\) , \( -7 a^{4} + 80 a^{3} + 150 a^{2} - 88 a - 112\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-5a-3\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+11a^{2}-6a-6\right){x}^{2}+\left(-22a^{4}+17a^{3}+104a^{2}-27a-59\right){x}-7a^{4}+80a^{3}+150a^{2}-88a-112$ |
| 32.1-b1 |
32.1-b |
$4$ |
$6$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( - 2^{13} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \) |
$1$ |
$16.58875164$ |
1.62611290 |
\( -\frac{35957895928428405}{8} a^{4} + \frac{63204719666240269}{8} a^{3} + \frac{41963621177125959}{2} a^{2} - \frac{127190457992394647}{8} a - \frac{47453986353676479}{8} \) |
\( \bigl[a\) , \( 3 a^{4} - 5 a^{3} - 15 a^{2} + 8 a + 8\) , \( -2 a^{4} + 4 a^{3} + 9 a^{2} - 9 a - 3\) , \( 105 a^{4} - 117 a^{3} - 549 a^{2} + 5 a + 45\) , \( 621 a^{4} - 523 a^{3} - 3381 a^{2} - 887 a - 3\bigr] \) |
${y}^2+a{x}{y}+\left(-2a^{4}+4a^{3}+9a^{2}-9a-3\right){y}={x}^{3}+\left(3a^{4}-5a^{3}-15a^{2}+8a+8\right){x}^{2}+\left(105a^{4}-117a^{3}-549a^{2}+5a+45\right){x}+621a^{4}-523a^{3}-3381a^{2}-887a-3$ |
| 32.1-b2 |
32.1-b |
$4$ |
$6$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( - 2^{15} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4031.066649$ |
1.62611290 |
\( -\frac{5074069}{64} a^{4} + \frac{8915197}{64} a^{3} + \frac{23743343}{64} a^{2} - \frac{564415}{2} a - \frac{6577431}{64} \) |
\( \bigl[a\) , \( 3 a^{4} - 5 a^{3} - 15 a^{2} + 8 a + 8\) , \( -2 a^{4} + 4 a^{3} + 9 a^{2} - 9 a - 3\) , \( -2 a^{3} + a^{2} + 10 a + 10\) , \( 7 a^{4} - 9 a^{3} - 36 a^{2} + 6 a + 8\bigr] \) |
${y}^2+a{x}{y}+\left(-2a^{4}+4a^{3}+9a^{2}-9a-3\right){y}={x}^{3}+\left(3a^{4}-5a^{3}-15a^{2}+8a+8\right){x}^{2}+\left(-2a^{3}+a^{2}+10a+10\right){x}+7a^{4}-9a^{3}-36a^{2}+6a+8$ |
| 32.1-b3 |
32.1-b |
$4$ |
$6$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4031.066649$ |
1.62611290 |
\( \frac{31}{8} a^{4} - \frac{5247}{8} a^{3} + \frac{11829}{8} a^{2} + \frac{4015}{4} a + \frac{10871}{8} \) |
\( \bigl[a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 5 a\) , \( 0\) , \( -7 a^{4} + 18 a^{3} + 15 a^{2} - 18 a - 5\) , \( -15 a^{4} + 43 a^{3} + 13 a^{2} - 28 a - 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+5a\right){x}^{2}+\left(-7a^{4}+18a^{3}+15a^{2}-18a-5\right){x}-15a^{4}+43a^{3}+13a^{2}-28a-8$ |
| 32.1-b4 |
32.1-b |
$4$ |
$6$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{20} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \) |
$1$ |
$16.58875164$ |
1.62611290 |
\( \frac{579356251697}{32} a^{4} - \frac{3379118016255}{64} a^{3} - \frac{476010816285}{32} a^{2} + \frac{338794798673}{8} a + \frac{755573591515}{64} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + a + 4\) , \( -2 a^{4} + 3 a^{3} + 11 a^{2} - 4 a - 7\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 5 a - 3\) , \( 63 a^{4} + 33 a^{3} - 452 a^{2} - 458 a - 95\) , \( 758 a^{4} + 157 a^{3} - 5015 a^{2} - 4837 a - 969\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+a+4\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-5a-3\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+11a^{2}-4a-7\right){x}^{2}+\left(63a^{4}+33a^{3}-452a^{2}-458a-95\right){x}+758a^{4}+157a^{3}-5015a^{2}-4837a-969$ |
| 32.1-c1 |
32.1-c |
$1$ |
$1$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{17} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$1$ |
$146.5590387$ |
2.48309088 |
\( \frac{71850708622137}{128} a^{4} - \frac{1519978420669}{32} a^{3} - \frac{436669641140547}{128} a^{2} - \frac{399719150434079}{128} a - \frac{19623159656159}{32} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a\) , \( -31 a^{4} + 97 a^{3} + 11 a^{2} - 85 a - 21\) , \( -377 a^{4} + 1057 a^{3} + 390 a^{2} - 768 a - 221\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+3\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-5a-1\right){x}^{2}+\left(-31a^{4}+97a^{3}+11a^{2}-85a-21\right){x}-377a^{4}+1057a^{3}+390a^{2}-768a-221$ |
| 32.1-d1 |
32.1-d |
$1$ |
$1$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{17} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.020333956$ |
$13127.92405$ |
3.23050127 |
\( -\frac{16387723}{8} a^{4} + \frac{44190629}{16} a^{3} + \frac{356053187}{32} a^{2} - \frac{104134767}{32} a - \frac{224790871}{32} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + a + 4\) , \( -a^{2} + 2 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -2 a^{4} + 10 a^{2} - 6\) , \( a^{4} - 3 a^{3} - 5 a^{2} + 3 a\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+a+4\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(-2a^{4}+10a^{2}-6\right){x}+a^{4}-3a^{3}-5a^{2}+3a$ |
| 32.1-e1 |
32.1-e |
$2$ |
$2$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{11} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$847.4282773$ |
2.05109095 |
\( \frac{13167672121}{16} a^{4} - \frac{4870593259}{2} a^{3} - \frac{9804461715}{16} a^{2} + \frac{32465717733}{16} a + \frac{1118584945}{2} \) |
\( \bigl[-2 a^{4} + 4 a^{3} + 9 a^{2} - 8 a - 4\) , \( a^{4} - a^{3} - 5 a^{2} - a + 1\) , \( a^{3} - a^{2} - 4 a\) , \( a^{4} + 8 a^{3} - 21 a^{2} - 25 a - 5\) , \( -25 a^{4} + 43 a^{3} + 70 a^{2} + 45 a + 8\bigr] \) |
${y}^2+\left(-2a^{4}+4a^{3}+9a^{2}-8a-4\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}-a+1\right){x}^{2}+\left(a^{4}+8a^{3}-21a^{2}-25a-5\right){x}-25a^{4}+43a^{3}+70a^{2}+45a+8$ |
| 32.1-e2 |
32.1-e |
$2$ |
$2$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{10} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$847.4282773$ |
2.05109095 |
\( 259733024097 a^{4} - \frac{665655696715}{2} a^{3} - \frac{5858930096627}{4} a^{2} + 412209754182 a + \frac{3691706405239}{4} \) |
\( \bigl[-2 a^{4} + 4 a^{3} + 9 a^{2} - 9 a - 4\) , \( -a^{4} + a^{3} + 5 a^{2} + a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 1\) , \( -157 a^{4} + 424 a^{3} + 203 a^{2} - 302 a - 91\) , \( -3032 a^{4} + 8388 a^{3} + 3357 a^{2} - 5885 a - 1716\bigr] \) |
${y}^2+\left(-2a^{4}+4a^{3}+9a^{2}-9a-4\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}+a\right){x}^{2}+\left(-157a^{4}+424a^{3}+203a^{2}-302a-91\right){x}-3032a^{4}+8388a^{3}+3357a^{2}-5885a-1716$ |
| 32.1-f1 |
32.1-f |
$2$ |
$3$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( - 2^{9} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$1168.829703$ |
0.943000564 |
\( -\frac{107009695}{8} a^{4} - \frac{188843213}{8} a^{3} + \frac{55450937}{8} a^{2} + \frac{37151727}{2} a + \frac{33898311}{8} \) |
\( \bigl[a^{4} - a^{3} - 6 a^{2} + 3\) , \( a^{4} - a^{3} - 6 a^{2} - a + 3\) , \( 0\) , \( 15 a^{4} - 16 a^{3} - 91 a^{2} + 11 a + 69\) , \( -30 a^{4} + 39 a^{3} + 168 a^{2} - 50 a - 104\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-6a^{2}+3\right){x}{y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}-a+3\right){x}^{2}+\left(15a^{4}-16a^{3}-91a^{2}+11a+69\right){x}-30a^{4}+39a^{3}+168a^{2}-50a-104$ |
| 32.1-f2 |
32.1-f |
$2$ |
$3$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( - 2^{11} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$4.809998781$ |
0.943000564 |
\( -25331900908525216490781779 a^{4} - \frac{383824734001039705996733901}{8} a^{3} + \frac{105150472223954757196879255}{8} a^{2} + \frac{304303272566410417438802361}{8} a + \frac{35013246100145623412557967}{4} \) |
\( \bigl[-2 a^{4} + 4 a^{3} + 9 a^{2} - 8 a - 4\) , \( 2 a^{4} - 3 a^{3} - 11 a^{2} + 6 a + 5\) , \( -a^{4} + 3 a^{3} + 3 a^{2} - 9 a - 1\) , \( -9 a^{4} - 32 a^{3} + 182 a^{2} + 3 a - 128\) , \( 10166 a^{4} - 28491 a^{3} - 10141 a^{2} + 19809 a + 5075\bigr] \) |
${y}^2+\left(-2a^{4}+4a^{3}+9a^{2}-8a-4\right){x}{y}+\left(-a^{4}+3a^{3}+3a^{2}-9a-1\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-11a^{2}+6a+5\right){x}^{2}+\left(-9a^{4}-32a^{3}+182a^{2}+3a-128\right){x}+10166a^{4}-28491a^{3}-10141a^{2}+19809a+5075$ |
| 32.1-g1 |
32.1-g |
$4$ |
$4$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( - 2^{9} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.111292171$ |
$3886.334334$ |
3.92570815 |
\( \frac{69382602123903923}{8} a^{4} + \frac{32853274221870833}{2} a^{3} - \frac{35995700876547337}{8} a^{2} - \frac{104188995035987245}{8} a - 2997073439095707 \) |
\( \bigl[a\) , \( a^{4} - a^{3} - 5 a^{2} + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a\) , \( -419 a^{4} + 529 a^{3} + 2370 a^{2} - 624 a - 1483\) , \( 1724 a^{4} - 2255 a^{3} - 9715 a^{2} + 3021 a + 6353\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-4a\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+1\right){x}^{2}+\left(-419a^{4}+529a^{3}+2370a^{2}-624a-1483\right){x}+1724a^{4}-2255a^{3}-9715a^{2}+3021a+6353$ |
| 32.1-g2 |
32.1-g |
$4$ |
$4$ |
5.5.170701.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$52.21215$ |
$(a^4-a^3-6a^2+a+3), (-a^4+a^3+5a^2-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.055646085$ |
$7772.668669$ |
3.92570815 |
\( \frac{141171703}{16} a^{4} + \frac{1112334659}{64} a^{3} - \frac{61838747}{16} a^{2} - \frac{909329733}{64} a - \frac{209059393}{64} \) |
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 3 a - 1\) , \( a^{4} - a^{3} - 6 a^{2} + a + 2\) , \( 1\) , \( 35 a^{4} - 64 a^{3} - 158 a^{2} + 133 a + 34\) , \( -176 a^{4} + 304 a^{3} + 832 a^{2} - 600 a - 255\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-3a-1\right){x}{y}+{y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+a+2\right){x}^{2}+\left(35a^{4}-64a^{3}-158a^{2}+133a+34\right){x}-176a^{4}+304a^{3}+832a^{2}-600a-255$ |
*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.
