| 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 |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$7.64485$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$549.8126126$ |
1.041790200 |
\( 3952 a^{3} - 3952 a^{2} - 15808 a - 5596 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(a^{3}-2a^{2}-3a+1\right){x}+a^{3}-2a^{2}-3a+1$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$7.64485$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$549.8126126$ |
1.041790200 |
\( -2559338505800317 a^{3} - 857138677706119 a^{2} + 15068979519102710 a + 15284041675437812 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( 26 a^{3} - 52 a^{2} - 73 a + 26\) , \( 130 a^{3} - 221 a^{2} - 392 a + 151\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(26a^{3}-52a^{2}-73a+26\right){x}+130a^{3}-221a^{2}-392a+151$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$7.64485$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$549.8126126$ |
1.041790200 |
\( -50135044 a^{3} + 50135044 a^{2} + 200540176 a + 71009018 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( 31 a^{3} - 57 a^{2} - 93 a + 36\) , \( 127 a^{3} - 227 a^{2} - 378 a + 147\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(31a^{3}-57a^{2}-93a+36\right){x}+127a^{3}-227a^{2}-378a+147$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$7.64485$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$34.36328829$ |
1.041790200 |
\( -4560667376911747 a^{3} + 7977144560418183 a^{2} + 13411044011745546 a - 5214821425600804 \) |
\( \bigl[a\) , \( -a^{2} + a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( 6 a^{3} + 20 a^{2} - 56 a - 130\) , \( -76 a^{3} - 15 a^{2} + 432 a + 394\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(6a^{3}+20a^{2}-56a-130\right){x}-76a^{3}-15a^{2}+432a+394$ |
| 8.1-b1 |
8.1-b |
$4$ |
$4$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$7.64485$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$549.8126126$ |
1.041790200 |
\( -4560667376911747 a^{3} + 7977144560418183 a^{2} + 13411044011745546 a - 5214821425600804 \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( 6 a^{3} + 22 a^{2} - 59 a - 135\) , \( 82 a^{3} + 36 a^{2} - 489 a - 527\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(6a^{3}+22a^{2}-59a-135\right){x}+82a^{3}+36a^{2}-489a-527$ |
| 8.1-b2 |
8.1-b |
$4$ |
$4$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$7.64485$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$549.8126126$ |
1.041790200 |
\( -50135044 a^{3} + 50135044 a^{2} + 200540176 a + 71009018 \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( 11 a^{3} + 17 a^{2} - 79 a - 125\) , \( 68 a^{3} + 59 a^{2} - 435 a - 575\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(11a^{3}+17a^{2}-79a-125\right){x}+68a^{3}+59a^{2}-435a-575$ |
| 8.1-b3 |
8.1-b |
$4$ |
$4$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$7.64485$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$549.8126126$ |
1.041790200 |
\( 3952 a^{3} - 3952 a^{2} - 15808 a - 5596 \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( a^{3} + 2 a^{2} - 9 a - 10\) , \( a^{3} + 2 a^{2} - 8 a - 12\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(a^{3}+2a^{2}-9a-10\right){x}+a^{3}+2a^{2}-8a-12$ |
| 8.1-b4 |
8.1-b |
$4$ |
$4$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$7.64485$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$34.36328829$ |
1.041790200 |
\( -2559338505800317 a^{3} - 857138677706119 a^{2} + 15068979519102710 a + 15284041675437812 \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a + 1\) , \( a\) , \( 26 a^{3} - 52 a^{2} - 74 a + 27\) , \( -104 a^{3} + 169 a^{2} + 319 a - 125\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(26a^{3}-52a^{2}-74a+27\right){x}-104a^{3}+169a^{2}+319a-125$ |
| 16.1-a1 |
16.1-a |
$6$ |
$8$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.33677$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$1288.286147$ |
1.220528460 |
\( 8000 \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 4 a - 2\) , \( 4 a^{3} - 3 a^{2} - 14 a - 2\) , \( 5 a^{2} + 2 a - 7\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(4a^{3}-3a^{2}-14a-2\right){x}+5a^{2}+2a-7$ |
| 16.1-a2 |
16.1-a |
$6$ |
$8$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.33677$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$1288.286147$ |
1.220528460 |
\( 8000 \) |
\( \bigl[a^{3} - 4 a - 2\) , \( -a^{3} + 4 a + 4\) , \( 0\) , \( -a^{3} - 2 a^{2} + 12 a + 15\) , \( 2 a^{3} - 6 a^{2} + 14\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}={x}^{3}+\left(-a^{3}+4a+4\right){x}^{2}+\left(-a^{3}-2a^{2}+12a+15\right){x}+2a^{3}-6a^{2}+14$ |
| 16.1-a3 |
16.1-a |
$6$ |
$8$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.33677$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$322.0715367$ |
1.220528460 |
\( 18473000 a^{3} - 18473000 a^{2} - 73892000 a + 26125000 \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 5 a + 3\) , \( 0\) , \( -6 a^{3} - 2 a^{2} + 32 a + 30\) , \( -29 a^{3} - 14 a^{2} + 162 a + 171\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{3}+5a+3\right){x}^{2}+\left(-6a^{3}-2a^{2}+32a+30\right){x}-29a^{3}-14a^{2}+162a+171$ |
| 16.1-a4 |
16.1-a |
$6$ |
$8$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.33677$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$322.0715367$ |
1.220528460 |
\( -18473000 a^{3} + 18473000 a^{2} + 73892000 a + 26125000 \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 4 a - 2\) , \( 23 a^{3} - 36 a^{2} - 62 a + 26\) , \( 76 a^{3} - 148 a^{2} - 240 a + 90\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(a^{3}-4a-3\right){x}^{2}+\left(23a^{3}-36a^{2}-62a+26\right){x}+76a^{3}-148a^{2}-240a+90$ |
| 16.1-a5 |
16.1-a |
$6$ |
$8$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.33677$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$322.0715367$ |
1.220528460 |
\( -18473000 a^{3} + 18473000 a^{2} + 73892000 a + 26125000 \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{2} + 3\) , \( a^{3} - 4 a - 2\) , \( 25 a^{3} - 12 a^{2} - 128 a - 54\) , \( -4 a^{3} + 104 a^{2} - 78 a - 476\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(25a^{3}-12a^{2}-128a-54\right){x}-4a^{3}+104a^{2}-78a-476$ |
| 16.1-a6 |
16.1-a |
$6$ |
$8$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$8.33677$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$322.0715367$ |
1.220528460 |
\( 18473000 a^{3} - 18473000 a^{2} - 73892000 a + 26125000 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - a^{2} - 4 a\) , \( -5 a^{3} + 26 a + 21\) , \( 22 a^{3} + 8 a^{2} - 130 a - 135\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(-5a^{3}+26a+21\right){x}+22a^{3}+8a^{2}-130a-135$ |
| 17.1-a1 |
17.1-a |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$361.5119434$ |
1.369992580 |
\( \frac{7182663766855915382472}{289} a^{3} + \frac{19289359099509254671960}{289} a^{2} + \frac{8706438693633454638096}{289} a - \frac{5349131458610150214808}{289} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} - 5 a - 3\) , \( 97 a^{3} + 62 a^{2} - 611 a - 740\) , \( 1462 a^{3} + 413 a^{2} - 8506 a - 8318\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{3}-5a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(97a^{3}+62a^{2}-611a-740\right){x}+1462a^{3}+413a^{2}-8506a-8318$ |
| 17.1-a2 |
17.1-a |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$361.5119434$ |
1.369992580 |
\( \frac{97563803260643371659320}{289} a^{3} - \frac{124035826127008541713752}{289} a^{2} - \frac{427692306803630602805264}{289} a + \frac{153483005739580870111784}{289} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{2} - a - 3\) , \( 193 a^{3} - 351 a^{2} - 552 a + 213\) , \( 2554 a^{3} - 4428 a^{2} - 7560 a + 2930\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(193a^{3}-351a^{2}-552a+213\right){x}+2554a^{3}-4428a^{2}-7560a+2930$ |
| 17.1-a3 |
17.1-a |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$723.0238868$ |
1.369992580 |
\( \frac{55615383938816}{4913} a^{3} - \frac{55615383938816}{4913} a^{2} - \frac{222461535755264}{4913} a + \frac{78652069441856}{4913} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( 34 a^{3} - 34 a^{2} - 137 a - 54\) , \( -112 a^{3} + 112 a^{2} + 446 a + 159\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(34a^{3}-34a^{2}-137a-54\right){x}-112a^{3}+112a^{2}+446a+159$ |
| 17.1-a4 |
17.1-a |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$723.0238868$ |
1.369992580 |
\( -\frac{3690752}{17} a^{3} + \frac{3690752}{17} a^{2} + \frac{14763008}{17} a + \frac{5287232}{17} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -a - 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(a^{3}-a^{2}-5a-1\right){x}-a-2$ |
| 17.1-a5 |
17.1-a |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{12} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$180.7559717$ |
1.369992580 |
\( -\frac{1522678220544}{24137569} a^{3} + \frac{1522678220544}{24137569} a^{2} + \frac{6090712882176}{24137569} a - \frac{2147745195712}{24137569} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{2} - 3\) , \( -15 a^{3} + 15 a^{2} + 59 a - 19\) , \( 33 a^{3} - 33 a^{2} - 133 a + 48\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-15a^{3}+15a^{2}+59a-19\right){x}+33a^{3}-33a^{2}-133a+48$ |
| 17.1-a6 |
17.1-a |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$180.7559717$ |
1.369992580 |
\( \frac{94464}{289} a^{3} - \frac{94464}{289} a^{2} - \frac{377856}{289} a + \frac{58688}{289} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{2} - 3\) , \( -a + 1\) , \( -a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-a+1\right){x}-a-1$ |
| 17.1-a7 |
17.1-a |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$361.5119434$ |
1.369992580 |
\( -\frac{823267912360}{17} a^{3} - \frac{275706088696}{17} a^{2} + \frac{4847298829872}{17} a + \frac{4916463879976}{17} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 18 a^{3} - 32 a^{2} - 56 a + 22\) , \( 28 a^{3} - 50 a^{2} - 82 a + 32\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(18a^{3}-32a^{2}-56a+22\right){x}+28a^{3}-50a^{2}-82a+32$ |
| 17.1-a8 |
17.1-a |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$361.5119434$ |
1.369992580 |
\( -\frac{1466988734040}{17} a^{3} + \frac{2565962735096}{17} a^{2} + \frac{4313727755728}{17} a - \frac{1677380126360}{17} \) |
\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 4 a - 3\) , \( 1\) , \( 6 a^{3} + 8 a^{2} - 40 a - 61\) , \( 11 a^{3} - 10 a^{2} - 51 a - 1\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-3\right){x}^{2}+\left(6a^{3}+8a^{2}-40a-61\right){x}+11a^{3}-10a^{2}-51a-1$ |
| 17.1-b1 |
17.1-b |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$988.4894573$ |
0.416222063 |
\( -\frac{1466988734040}{17} a^{3} + \frac{2565962735096}{17} a^{2} + \frac{4313727755728}{17} a - \frac{1677380126360}{17} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{3} - 5 a - 3\) , \( 4 a^{3} + 11 a^{2} - 32 a - 63\) , \( 3 a^{3} + 13 a^{2} - 27 a - 72\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{3}-5a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+3\right){x}^{2}+\left(4a^{3}+11a^{2}-32a-63\right){x}+3a^{3}+13a^{2}-27a-72$ |
| 17.1-b2 |
17.1-b |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$988.4894573$ |
0.416222063 |
\( -\frac{823267912360}{17} a^{3} - \frac{275706088696}{17} a^{2} + \frac{4847298829872}{17} a + \frac{4916463879976}{17} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a + 1\) , \( 15 a^{3} - 27 a^{2} - 45 a + 18\) , \( 11 a^{3} - 23 a^{2} - 36 a + 14\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(15a^{3}-27a^{2}-45a+18\right){x}+11a^{3}-23a^{2}-36a+14$ |
| 17.1-b3 |
17.1-b |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$24.40714709$ |
0.416222063 |
\( \frac{55615383938816}{4913} a^{3} - \frac{55615383938816}{4913} a^{2} - \frac{222461535755264}{4913} a + \frac{78652069441856}{4913} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 33 a^{3} - 33 a^{2} - 132 a - 53\) , \( 112 a^{3} - 112 a^{2} - 448 a - 163\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}-{x}^{2}+\left(33a^{3}-33a^{2}-132a-53\right){x}+112a^{3}-112a^{2}-448a-163$ |
| 17.1-b4 |
17.1-b |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{12} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$6.101786773$ |
0.416222063 |
\( -\frac{1522678220544}{24137569} a^{3} + \frac{1522678220544}{24137569} a^{2} + \frac{6090712882176}{24137569} a - \frac{2147745195712}{24137569} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -14 a^{3} + 14 a^{2} + 56 a - 19\) , \( -48 a^{3} + 48 a^{2} + 192 a - 69\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(-14a^{3}+14a^{2}+56a-19\right){x}-48a^{3}+48a^{2}+192a-69$ |
| 17.1-b5 |
17.1-b |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$494.2447286$ |
0.416222063 |
\( \frac{94464}{289} a^{3} - \frac{94464}{289} a^{2} - \frac{377856}{289} a + \frac{58688}{289} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(a^{3}-a^{2}-4a+1\right){x}$ |
| 17.1-b6 |
17.1-b |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1976.978914$ |
0.416222063 |
\( -\frac{3690752}{17} a^{3} + \frac{3690752}{17} a^{2} + \frac{14763008}{17} a + \frac{5287232}{17} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -2 a^{3} + 2 a^{2} + 8 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-2a^{3}+2a^{2}+8a-1\right){x}-a^{3}+a^{2}+4a-1$ |
| 17.1-b7 |
17.1-b |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$12.20357354$ |
0.416222063 |
\( \frac{97563803260643371659320}{289} a^{3} - \frac{124035826127008541713752}{289} a^{2} - \frac{427692306803630602805264}{289} a + \frac{153483005739580870111784}{289} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 4 a + 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 193 a^{3} - 352 a^{2} - 551 a + 216\) , \( -2037 a^{3} + 3532 a^{2} + 6029 a - 2347\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(193a^{3}-352a^{2}-551a+216\right){x}-2037a^{3}+3532a^{2}+6029a-2347$ |
| 17.1-b8 |
17.1-b |
$8$ |
$12$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$8.40019$ |
$(-a^3+2a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$12.20357354$ |
0.416222063 |
\( \frac{7182663766855915382472}{289} a^{3} + \frac{19289359099509254671960}{289} a^{2} + \frac{8706438693633454638096}{289} a - \frac{5349131458610150214808}{289} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} - 3\) , \( 98 a^{3} + 60 a^{2} - 613 a - 736\) , \( -1364 a^{3} - 352 a^{2} + 7891 a + 7577\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(98a^{3}+60a^{2}-613a-736\right){x}-1364a^{3}-352a^{2}+7891a+7577$ |
| 28.1-a1 |
28.1-a |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{8} \cdot 7^{3} \) |
$8.94083$ |
$(a), (-a^3+a^2+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$14.97737217$ |
1.532480479 |
\( \frac{3041167459768576}{343} a^{3} - \frac{3866330984561280}{343} a^{2} - \frac{13331621928344576}{343} a + \frac{4784240827520128}{343} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{3} - a^{2} - 4 a\) , \( -62 a^{3} + 96 a^{2} + 258 a - 167\) , \( -361 a^{3} + 508 a^{2} + 1536 a - 797\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-62a^{3}+96a^{2}+258a-167\right){x}-361a^{3}+508a^{2}+1536a-797$ |
| 28.1-a2 |
28.1-a |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{8} \cdot 7 \) |
$8.94083$ |
$(a), (-a^3+a^2+5a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$1213.167146$ |
1.532480479 |
\( \frac{64256}{7} a^{3} - \frac{82048}{7} a^{2} - \frac{286208}{7} a + \frac{115840}{7} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{3} - a^{2} - 4 a\) , \( -2 a^{3} + 6 a^{2} + 8 a - 7\) , \( -a^{3} + 4 a^{2} + 6 a - 3\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-2a^{3}+6a^{2}+8a-7\right){x}-a^{3}+4a^{2}+6a-3$ |
| 28.1-a3 |
28.1-a |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{6} \) |
$8.94083$ |
$(a), (-a^3+a^2+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$7.488686088$ |
1.532480479 |
\( -\frac{569382817064459200}{117649} a^{3} + \frac{995917381958663392}{117649} a^{2} + \frac{1674320458640220800}{117649} a - \frac{651051605141292448}{117649} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a\) , \( -15 a^{3} + 19 a^{2} + 60 a - 37\) , \( -53 a^{3} + 65 a^{2} + 220 a - 99\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(-15a^{3}+19a^{2}+60a-37\right){x}-53a^{3}+65a^{2}+220a-99$ |
| 28.1-a4 |
28.1-a |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$8.94083$ |
$(a), (-a^3+a^2+5a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$606.5835731$ |
1.532480479 |
\( -\frac{285760}{49} a^{3} + \frac{658016}{49} a^{2} + \frac{1036544}{49} a - \frac{332704}{49} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a\) , \( -a^{2} + 3\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(-a^{2}+3\right){x}-1$ |
| 28.1-b1 |
28.1-b |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{8} \cdot 7^{3} \) |
$8.94083$ |
$(a), (-a^3+a^2+5a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.144076130$ |
$904.5057417$ |
1.975417610 |
\( \frac{3041167459768576}{343} a^{3} - \frac{3866330984561280}{343} a^{2} - \frac{13331621928344576}{343} a + \frac{4784240827520128}{343} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 6 a - 4\) , \( a^{2} - 2\) , \( -60 a^{3} + 92 a^{2} + 252 a - 162\) , \( 311 a^{3} - 452 a^{2} - 1300 a + 773\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-6a-4\right){x}^{2}+\left(-60a^{3}+92a^{2}+252a-162\right){x}+311a^{3}-452a^{2}-1300a+773$ |
| 28.1-b2 |
28.1-b |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{8} \cdot 7 \) |
$8.94083$ |
$(a), (-a^3+a^2+5a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.048025376$ |
$904.5057417$ |
1.975417610 |
\( \frac{64256}{7} a^{3} - \frac{82048}{7} a^{2} - \frac{286208}{7} a + \frac{115840}{7} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 6 a - 4\) , \( a^{2} - 2\) , \( 2 a^{2} + 2 a - 2\) , \( a^{3} + 2 a^{2} - 1\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-6a-4\right){x}^{2}+\left(2a^{2}+2a-2\right){x}+a^{3}+2a^{2}-1$ |
| 28.1-b3 |
28.1-b |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{6} \) |
$8.94083$ |
$(a), (-a^3+a^2+5a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.072038065$ |
$904.5057417$ |
1.975417610 |
\( -\frac{569382817064459200}{117649} a^{3} + \frac{995917381958663392}{117649} a^{2} + \frac{1674320458640220800}{117649} a - \frac{651051605141292448}{117649} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{3} - 5 a - 2\) , \( -16 a^{3} + 21 a^{2} + 63 a - 41\) , \( 53 a^{3} - 65 a^{2} - 221 a + 96\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-16a^{3}+21a^{2}+63a-41\right){x}+53a^{3}-65a^{2}-221a+96$ |
| 28.1-b4 |
28.1-b |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$8.94083$ |
$(a), (-a^3+a^2+5a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.024012688$ |
$904.5057417$ |
1.975417610 |
\( -\frac{285760}{49} a^{3} + \frac{658016}{49} a^{2} + \frac{1036544}{49} a - \frac{332704}{49} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{3} - 5 a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( -a - 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-a^{3}+a^{2}+3a-1\right){x}-a-2$ |
| 28.2-a1 |
28.2-a |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( - 2^{8} \cdot 7 \) |
$8.94083$ |
$(a), (a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$1213.167146$ |
1.532480479 |
\( -\frac{512}{7} a^{3} + \frac{18304}{7} a^{2} + \frac{31232}{7} a + \frac{9088}{7} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{2} - 2\) , \( -a^{3} + 3 a^{2} + 2 a - 4\) , \( a^{2} - 1\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-a^{3}+3a^{2}+2a-4\right){x}+a^{2}-1$ |
| 28.2-a2 |
28.2-a |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( - 2^{8} \cdot 7^{3} \) |
$8.94083$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$14.97737217$ |
1.532480479 |
\( \frac{223888320912896}{343} a^{3} + \frac{601275203879808}{343} a^{2} + \frac{271398805618688}{343} a - \frac{166740321236096}{343} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{2} - 2\) , \( 9 a^{3} - 37 a^{2} - 48 a + 16\) , \( 28 a^{3} - 241 a^{2} - 252 a + 109\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(9a^{3}-37a^{2}-48a+16\right){x}+28a^{3}-241a^{2}-252a+109$ |
| 28.2-a3 |
28.2-a |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{6} \) |
$8.94083$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$7.488686088$ |
1.532480479 |
\( -\frac{319524496893666816}{117649} a^{3} - \frac{107010068000537376}{117649} a^{2} + \frac{1881308797192283264}{117649} a + \frac{1908155784223932704}{117649} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( -6 a^{3} + a^{2} + 24 a - 11\) , \( -20 a^{3} + 7 a^{2} + 72 a - 25\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(-6a^{3}+a^{2}+24a-11\right){x}-20a^{3}+7a^{2}+72a-25$ |
| 28.2-a4 |
28.2-a |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$8.94083$ |
$(a), (a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$606.5835731$ |
1.532480479 |
\( \frac{352256}{49} a^{3} - \frac{724512}{49} a^{2} - \frac{1302528}{49} a + \frac{1900832}{49} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 2 a^{2} - 4 a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(-a^{3}+a^{2}+4a-1\right){x}+a^{3}-2a^{2}-4a+1$ |
| 28.2-b1 |
28.2-b |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( - 2^{8} \cdot 7 \) |
$8.94083$ |
$(a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.048025376$ |
$904.5057417$ |
1.975417610 |
\( -\frac{512}{7} a^{3} + \frac{18304}{7} a^{2} + \frac{31232}{7} a + \frac{9088}{7} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 6 a - 4\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} + a^{2} + 1\) , \( a^{3} + 2 a^{2} - 2\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-6a-4\right){x}^{2}+\left(a^{3}+a^{2}+1\right){x}+a^{3}+2a^{2}-2$ |
| 28.2-b2 |
28.2-b |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( - 2^{8} \cdot 7^{3} \) |
$8.94083$ |
$(a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.144076130$ |
$904.5057417$ |
1.975417610 |
\( \frac{223888320912896}{343} a^{3} + \frac{601275203879808}{343} a^{2} + \frac{271398805618688}{343} a - \frac{166740321236096}{343} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 6 a - 4\) , \( a^{3} - a^{2} - 4 a\) , \( 11 a^{3} - 39 a^{2} - 50 a + 21\) , \( -27 a^{3} + 104 a^{2} + 122 a - 52\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-6a-4\right){x}^{2}+\left(11a^{3}-39a^{2}-50a+21\right){x}-27a^{3}+104a^{2}+122a-52$ |
| 28.2-b3 |
28.2-b |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{6} \) |
$8.94083$ |
$(a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.072038065$ |
$904.5057417$ |
1.975417610 |
\( -\frac{319524496893666816}{117649} a^{3} - \frac{107010068000537376}{117649} a^{2} + \frac{1881308797192283264}{117649} a + \frac{1908155784223932704}{117649} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{2} - a - 2\) , \( -7 a^{3} + 3 a^{2} + 27 a - 13\) , \( 21 a^{3} - 9 a^{2} - 76 a + 25\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-7a^{3}+3a^{2}+27a-13\right){x}+21a^{3}-9a^{2}-76a+25$ |
| 28.2-b4 |
28.2-b |
$4$ |
$6$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$8.94083$ |
$(a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.024012688$ |
$904.5057417$ |
1.975417610 |
\( \frac{352256}{49} a^{3} - \frac{724512}{49} a^{2} - \frac{1302528}{49} a + \frac{1900832}{49} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{2} - a - 2\) , \( -2 a^{3} + 3 a^{2} + 7 a - 3\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-2a^{3}+3a^{2}+7a-3\right){x}-1$ |
| 31.1-a1 |
31.1-a |
$6$ |
$8$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$9.05531$ |
$(-a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$131.1189419$ |
0.993781704 |
\( \frac{103264834192808}{961} a^{3} - \frac{128472113774504}{961} a^{2} - \frac{461176334853008}{961} a + \frac{164980369235848}{961} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - 3\) , \( 16 a^{3} - 28 a^{2} - 41 a + 27\) , \( -104 a^{3} + 56 a^{2} + 195 a - 57\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(16a^{3}-28a^{2}-41a+27\right){x}-104a^{3}+56a^{2}+195a-57$ |
| 31.1-a2 |
31.1-a |
$6$ |
$8$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$9.05531$ |
$(-a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$262.2378838$ |
0.993781704 |
\( -\frac{18804980776796280}{31} a^{3} - \frac{6297863001957416}{31} a^{2} + \frac{110720705231833392}{31} a + \frac{112300728541021592}{31} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 9 a^{3} - 19 a^{2} - 17 a + 6\) , \( 81 a^{3} - 133 a^{2} - 266 a + 101\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(9a^{3}-19a^{2}-17a+6\right){x}+81a^{3}-133a^{2}-266a+101$ |
| 31.1-a3 |
31.1-a |
$6$ |
$8$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{4} \) |
$9.05531$ |
$(-a^2+a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$524.4757676$ |
0.993781704 |
\( \frac{143974739712}{923521} a^{3} - \frac{165260773632}{923521} a^{2} - \frac{675177243648}{923521} a + \frac{247632688448}{923521} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + 5 a^{2} + a - 21\) , \( -9 a^{3} + 3 a^{2} + 47 a + 25\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(-a^{3}+5a^{2}+a-21\right){x}-9a^{3}+3a^{2}+47a+25$ |
| 31.1-a4 |
31.1-a |
$6$ |
$8$ |
4.4.4352.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$9.05531$ |
$(-a^2+a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$524.4757676$ |
0.993781704 |
\( \frac{16835518720}{961} a^{3} + \frac{65046477056}{961} a^{2} + \frac{80314582016}{961} a + \frac{31568802112}{961} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 1\) , \( 8 a^{3} + 6 a^{2} - 51 a - 62\) , \( -31 a^{3} - 9 a^{2} + 181 a + 179\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(8a^{3}+6a^{2}-51a-62\right){x}-31a^{3}-9a^{2}+181a+179$ |
*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.
