| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$6$ |
$99$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.21511$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$6.566833655$ |
0.517004069 |
\( 6548115718144 a^{3} - 6548115718144 a^{2} - 45836810027008 a - 22082088337408 \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( 1\) , \( -714 a^{3} + 2020 a^{2} + 596 a - 394\) , \( -11736 a^{3} + 33145 a^{2} + 9957 a - 6439\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-1\right){x}^{2}+\left(-714a^{3}+2020a^{2}+596a-394\right){x}-11736a^{3}+33145a^{2}+9957a-6439$ |
| 1.1-a2 |
1.1-a |
$6$ |
$99$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.21511$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$6.566833655$ |
0.517004069 |
\( -6548115718144 a^{3} + 6548115718144 a^{2} + 45836810027008 a - 15533972619264 \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 6 a - 2\) , \( 1\) , \( -13 a^{3} + 64 a^{2} + 149 a - 20\) , \( -23 a^{3} + 212 a^{2} + 374 a - 163\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{3}-a^{2}-6a-2\right){x}^{2}+\left(-13a^{3}+64a^{2}+149a-20\right){x}-23a^{3}+212a^{2}+374a-163$ |
| 1.1-a3 |
1.1-a |
$6$ |
$99$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.21511$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$531.9135261$ |
0.517004069 |
\( -6548115718144 a^{3} + 6548115718144 a^{2} + 45836810027008 a - 15533972619264 \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 7 a - 1\) , \( 1\) , \( -25 a^{3} + 25 a^{2} + 175 a + 85\) , \( 72 a^{3} - 72 a^{2} - 504 a - 243\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{3}-a^{2}-7a-1\right){x}^{2}+\left(-25a^{3}+25a^{2}+175a+85\right){x}+72a^{3}-72a^{2}-504a-243$ |
| 1.1-a4 |
1.1-a |
$6$ |
$99$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.21511$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$531.9135261$ |
0.517004069 |
\( -32768 \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 6 a - 2\) , \( 1\) , \( -3 a^{3} - 6 a^{2} - a\) , \( 13 a^{3} + 34 a^{2} + 20 a + 2\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{3}-a^{2}-6a-2\right){x}^{2}+\left(-3a^{3}-6a^{2}-a\right){x}+13a^{3}+34a^{2}+20a+2$ |
| 1.1-a5 |
1.1-a |
$6$ |
$99$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.21511$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$531.9135261$ |
0.517004069 |
\( -32768 \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( 1\) , \( 156 a^{3} - 440 a^{2} - 134 a + 86\) , \( -2586 a^{3} + 7303 a^{2} + 2195 a - 1418\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-1\right){x}^{2}+\left(156a^{3}-440a^{2}-134a+86\right){x}-2586a^{3}+7303a^{2}+2195a-1418$ |
| 1.1-a6 |
1.1-a |
$6$ |
$99$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.21511$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$531.9135261$ |
0.517004069 |
\( 6548115718144 a^{3} - 6548115718144 a^{2} - 45836810027008 a - 22082088337408 \) |
\( \bigl[0\) , \( -a^{3} + a^{2} + 7 a\) , \( 1\) , \( 25 a^{3} - 25 a^{2} - 175 a + 60\) , \( -72 a^{3} + 72 a^{2} + 504 a - 171\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(25a^{3}-25a^{2}-175a+60\right){x}-72a^{3}+72a^{2}+504a-171$ |
| 4.1-a1 |
4.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1.174111573$ |
$190.7995851$ |
1.959666788 |
\( -17212656600 a^{3} + 48609445005 a^{2} + 14609887056 a - 9436492467 \) |
\( \bigl[a^{2} - 2 a - 3\) , \( 2 a^{3} - 3 a^{2} - 9 a\) , \( 0\) , \( -38 a^{3} + 58 a^{2} + 194 a - 69\) , \( 108 a^{3} - 169 a^{2} - 559 a + 198\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}={x}^{3}+\left(2a^{3}-3a^{2}-9a\right){x}^{2}+\left(-38a^{3}+58a^{2}+194a-69\right){x}+108a^{3}-169a^{2}-559a+198$ |
| 4.1-a2 |
4.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.14788$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 1 \) |
$2.348223147$ |
$381.5991703$ |
1.959666788 |
\( -33162183 a^{3} + 22342392 a^{2} + 206098425 a + 100819296 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( -7 a^{3} - 14 a^{2} - a + 1\) , \( -7 a^{3} - 10 a^{2} + 5 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{3}+2a^{2}+5a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}+\left(-7a^{3}-14a^{2}-a+1\right){x}-7a^{3}-10a^{2}+5a-1$ |
| 4.1-a3 |
4.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$4.696446295$ |
$47.69989629$ |
1.959666788 |
\( -5624100187275240 a^{3} + 3776339202293655 a^{2} + 34985292436389996 a + 17118287036760807 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( -72 a^{3} - 159 a^{2} - 41 a + 16\) , \( 1682 a^{3} + 3425 a^{2} + 338 a - 572\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{3}+2a^{2}+5a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}+\left(-72a^{3}-159a^{2}-41a+16\right){x}+1682a^{3}+3425a^{2}+338a-572$ |
| 4.1-a4 |
4.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.391370524$ |
$1717.196266$ |
1.959666788 |
\( 57269264139 a^{3} - 88666052544 a^{2} - 295006139829 a + 104462317224 \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( -2 a^{3} + 3 a^{2} + 9 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( -4 a^{3} + 6 a^{2} + 18 a - 4\) , \( 14 a^{3} - 22 a^{2} - 72 a + 26\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(-a^{3}+2a^{2}+5a-2\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a-1\right){x}^{2}+\left(-4a^{3}+6a^{2}+18a-4\right){x}+14a^{3}-22a^{2}-72a+26$ |
| 4.1-a5 |
4.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1.565482098$ |
$429.2990666$ |
1.959666788 |
\( 607069672243029 a^{3} + 1240691312738556 a^{2} + 133921168835481 a - 199448732646972 \) |
\( \bigl[a^{3} - a^{2} - 6 a\) , \( -2 a^{3} + 3 a^{2} + 9 a - 1\) , \( a + 1\) , \( 147 a^{3} - 102 a^{2} - 929 a - 453\) , \( 1766 a^{3} - 1166 a^{2} - 10943 a - 5358\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a-1\right){x}^{2}+\left(147a^{3}-102a^{2}-929a-453\right){x}+1766a^{3}-1166a^{2}-10943a-5358$ |
| 4.1-a6 |
4.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.14788$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 3 \) |
$0.782741049$ |
$3434.392533$ |
1.959666788 |
\( 3694464 a^{3} + 7125327 a^{2} + 175608 a - 956097 \) |
\( \bigl[a^{3} - a^{2} - 6 a\) , \( -2 a^{3} + 3 a^{2} + 9 a - 1\) , \( a + 1\) , \( 12 a^{3} - 7 a^{2} - 79 a - 38\) , \( 15 a^{3} - 9 a^{2} - 95 a - 47\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a-1\right){x}^{2}+\left(12a^{3}-7a^{2}-79a-38\right){x}+15a^{3}-9a^{2}-95a-47$ |
| 4.1-a7 |
4.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.391370524$ |
$1717.196266$ |
1.959666788 |
\( -5472495 a^{3} + 15453180 a^{2} + 4644621 a - 2998188 \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -34 a^{3} + 52 a^{2} + 174 a - 61\) , \( 16 a^{3} - 25 a^{2} - 83 a + 29\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-34a^{3}+52a^{2}+174a-61\right){x}+16a^{3}-25a^{2}-83a+29$ |
| 4.1-a8 |
4.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1.174111573$ |
$190.7995851$ |
1.959666788 |
\( 18209664 a^{3} - 28190349 a^{2} - 93804804 a + 33203763 \) |
\( \bigl[a + 1\) , \( 2 a^{3} - 3 a^{2} - 10 a + 1\) , \( a + 1\) , \( 2 a^{3} - 3 a^{2} - 10 a + 4\) , \( a^{3} - a^{2} - 5 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-10a+1\right){x}^{2}+\left(2a^{3}-3a^{2}-10a+4\right){x}+a^{3}-a^{2}-5a+1$ |
| 4.1-b1 |
4.1-b |
$2$ |
$3$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.14788$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.122182644$ |
$208.7427694$ |
0.892434582 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a + 1\) , \( -a^{3} - 2 a^{2} - 2 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-a^{3}+2a^{2}+3a+1\right){x}-a^{3}-2a^{2}-2a-1$ |
| 4.1-b2 |
4.1-b |
$2$ |
$3$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.14788$ |
$(a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.040727548$ |
$1878.684925$ |
0.892434582 |
\( 0 \) |
\( \bigl[0\) , \( a^{3} - 2 a^{2} - 5 a + 3\) , \( a^{2} - a - 2\) , \( 2 a^{3} - 3 a^{2} - 10 a + 4\) , \( 12 a^{3} + 19 a^{2} - 5 a - 2\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a+3\right){x}^{2}+\left(2a^{3}-3a^{2}-10a+4\right){x}+12a^{3}+19a^{2}-5a-2$ |
| 4.1-c1 |
4.1-c |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
|
\( 1 \) |
$1$ |
$190.7995851$ |
1.959666788 |
\( 57269264139 a^{3} - 88666052544 a^{2} - 295006139829 a + 104462317224 \) |
\( \bigl[-a^{3} + 2 a^{2} + 5 a - 2\) , \( -2 a^{3} + 3 a^{2} + 9 a - 2\) , \( 0\) , \( 14 a^{3} - 34 a^{2} - 26 a - 1\) , \( -28 a^{3} + 89 a^{2} - a - 32\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+5a-2\right){x}{y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a-2\right){x}^{2}+\left(14a^{3}-34a^{2}-26a-1\right){x}-28a^{3}+89a^{2}-a-32$ |
| 4.1-c2 |
4.1-c |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
|
\( 3 \) |
$1$ |
$1717.196266$ |
1.959666788 |
\( -17212656600 a^{3} + 48609445005 a^{2} + 14609887056 a - 9436492467 \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( 2 a^{3} - 3 a^{2} - 9 a + 1\) , \( a^{2} - 2 a - 3\) , \( 4 a^{3} - 6 a^{2} - 18 a\) , \( -4 a^{3} + 12 a^{2} + 2 a - 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-9a+1\right){x}^{2}+\left(4a^{3}-6a^{2}-18a\right){x}-4a^{3}+12a^{2}+2a-4$ |
| 4.1-c3 |
4.1-c |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
|
\( 1 \) |
$1$ |
$190.7995851$ |
1.959666788 |
\( -5472495 a^{3} + 15453180 a^{2} + 4644621 a - 2998188 \) |
\( \bigl[a^{3} - a^{2} - 6 a\) , \( -2 a^{3} + 3 a^{2} + 9 a - 1\) , \( a^{3} - a^{2} - 6 a\) , \( -3 a^{3} + 4 a^{2} + 15 a + 3\) , \( -2 a^{3} + 2 a^{2} + 11 a + 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a-1\right){x}^{2}+\left(-3a^{3}+4a^{2}+15a+3\right){x}-2a^{3}+2a^{2}+11a+4$ |
| 4.1-c4 |
4.1-c |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
|
\( 3 \) |
$1$ |
$1717.196266$ |
1.959666788 |
\( 18209664 a^{3} - 28190349 a^{2} - 93804804 a + 33203763 \) |
\( \bigl[a^{3} - a^{2} - 6 a\) , \( 0\) , \( a^{3} - a^{2} - 6 a\) , \( 10 a^{3} - 28 a^{2} - 8 a + 3\) , \( -5 a^{3} + 14 a^{2} + 5 a - 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(10a^{3}-28a^{2}-8a+3\right){x}-5a^{3}+14a^{2}+5a-4$ |
| 4.1-c5 |
4.1-c |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
|
\( 1 \) |
$1$ |
$47.69989629$ |
1.959666788 |
\( 607069672243029 a^{3} + 1240691312738556 a^{2} + 133921168835481 a - 199448732646972 \) |
\( \bigl[a + 1\) , \( -a\) , \( a^{3} - a^{2} - 6 a\) , \( 17 a^{3} - 27 a^{2} - 165 a - 106\) , \( -260 a^{3} + 42 a^{2} + 1171 a + 418\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}-a{x}^{2}+\left(17a^{3}-27a^{2}-165a-106\right){x}-260a^{3}+42a^{2}+1171a+418$ |
| 4.1-c6 |
4.1-c |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.14788$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
|
\( 1 \) |
$1$ |
$381.5991703$ |
1.959666788 |
\( 3694464 a^{3} + 7125327 a^{2} + 175608 a - 956097 \) |
\( \bigl[a + 1\) , \( -a\) , \( a^{3} - a^{2} - 6 a\) , \( -8 a^{3} + 13 a^{2} + 35 a - 26\) , \( -27 a^{3} + 38 a^{2} + 133 a - 48\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}-a{x}^{2}+\left(-8a^{3}+13a^{2}+35a-26\right){x}-27a^{3}+38a^{2}+133a-48$ |
| 4.1-c7 |
4.1-c |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.14788$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
|
\( 3 \) |
$1$ |
$429.2990666$ |
1.959666788 |
\( -5624100187275240 a^{3} + 3776339202293655 a^{2} + 34985292436389996 a + 17118287036760807 \) |
\( \bigl[a + 1\) , \( 2 a^{3} - 3 a^{2} - 10 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - 46 a^{2} - 109 a - 37\) , \( -254 a^{3} - 346 a^{2} + 358 a + 262\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-10a+1\right){x}^{2}+\left(a^{3}-46a^{2}-109a-37\right){x}-254a^{3}-346a^{2}+358a+262$ |
| 4.1-c8 |
4.1-c |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.14788$ |
$(a+1)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
|
\( 3 \) |
$1$ |
$3434.392533$ |
1.959666788 |
\( -33162183 a^{3} + 22342392 a^{2} + 206098425 a + 100819296 \) |
\( \bigl[a + 1\) , \( 2 a^{3} - 3 a^{2} - 10 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - 6 a^{2} - 14 a + 3\) , \( -2 a^{3} - 4 a^{2} + 3 a + 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-10a+1\right){x}^{2}+\left(a^{3}-6a^{2}-14a+3\right){x}-2a^{3}-4a^{2}+3a+6$ |
| 6.1-a1 |
6.1-a |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$1.754908944$ |
1.964988414 |
\( -\frac{488762023013849869}{3} a^{3} + \frac{219433826309245451}{2} a^{2} + \frac{2025318697845277225}{2} a + \frac{2972095626608234357}{6} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( 129 a^{3} - 109 a^{2} - 753 a - 373\) , \( 1326 a^{3} - 994 a^{2} - 8022 a - 3893\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(129a^{3}-109a^{2}-753a-373\right){x}+1326a^{3}-994a^{2}-8022a-3893$ |
| 6.1-a2 |
6.1-a |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$1.754908944$ |
1.964988414 |
\( \frac{54205374865165069}{3} a^{3} + \frac{70270605789877749}{2} a^{2} + \frac{2612326848585175}{2} a - \frac{29174571749575829}{6} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -41 a^{3} + 21 a^{2} + 137 a - 83\) , \( -266 a^{3} - 66 a^{2} + 602 a - 309\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(-41a^{3}+21a^{2}+137a-83\right){x}-266a^{3}-66a^{2}+602a-309$ |
| 6.1-a3 |
6.1-a |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$28.07854310$ |
1.964988414 |
\( -\frac{1814298623}{12} a^{3} + \frac{1814298623}{12} a^{2} + \frac{12700090361}{12} a + \frac{1663895809}{3} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( 4 a^{3} - 4 a^{2} - 28 a - 28\) , \( 20 a^{3} - 20 a^{2} - 140 a - 79\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(4a^{3}-4a^{2}-28a-28\right){x}+20a^{3}-20a^{2}-140a-79$ |
| 6.1-a4 |
6.1-a |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$449.2566896$ |
1.964988414 |
\( -\frac{65471}{16} a^{3} + \frac{65471}{16} a^{2} + \frac{458297}{16} a + \frac{127585}{6} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a - 3\) , \( -3\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(-a^{3}+a^{2}+7a-3\right){x}-3$ |
| 6.1-a5 |
6.1-a |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{4} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1797.026758$ |
1.964988414 |
\( -\frac{1547627}{2} a^{3} + \frac{1547627}{2} a^{2} + \frac{10833389}{2} a + \frac{7829167}{3} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 1\) , \( a^{2} - a - 3\) , \( 4 a^{3} - 4 a^{2} - 28 a + 9\) , \( 23 a^{3} - 23 a^{2} - 161 a + 52\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+{x}^{2}+\left(4a^{3}-4a^{2}-28a+9\right){x}+23a^{3}-23a^{2}-161a+52$ |
| 6.1-a6 |
6.1-a |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{8} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1797.026758$ |
1.964988414 |
\( \frac{11767}{12} a^{3} - \frac{11767}{12} a^{2} - \frac{82369}{12} a + \frac{47491}{9} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a + 1\) , \( 28 a^{3} - 83 a^{2} - 13 a + 22\) , \( -194 a^{3} + 546 a^{2} + 168 a - 104\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+1\right){x}^{2}+\left(28a^{3}-83a^{2}-13a+22\right){x}-194a^{3}+546a^{2}+168a-104$ |
| 6.1-a7 |
6.1-a |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{16} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$449.2566896$ |
1.964988414 |
\( \frac{573965017}{54} a^{3} - \frac{573965017}{54} a^{2} - \frac{4017755119}{54} a + \frac{2042488003}{81} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a + 1\) , \( 463 a^{3} - 1313 a^{2} - 378 a + 262\) , \( -13942 a^{3} + 39369 a^{2} + 11842 a - 7637\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+1\right){x}^{2}+\left(463a^{3}-1313a^{2}-378a+262\right){x}-13942a^{3}+39369a^{2}+11842a-7637$ |
| 6.1-a8 |
6.1-a |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$112.3141724$ |
1.964988414 |
\( \frac{34451}{768} a^{3} - \frac{34451}{768} a^{2} - \frac{241157}{768} a + \frac{10651}{96} \) |
\( \bigl[a\) , \( -2 a^{3} + 3 a^{2} + 11 a\) , \( a^{2} - 2 a - 3\) , \( a^{3} - 3 a + 7\) , \( -5 a^{3} - 5 a^{2} + 7 a - 4\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+11a\right){x}^{2}+\left(a^{3}-3a+7\right){x}-5a^{3}-5a^{2}+7a-4$ |
| 6.1-b1 |
6.1-b |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{16} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.159029436$ |
$37.19196527$ |
1.655663451 |
\( \frac{573965017}{54} a^{3} - \frac{573965017}{54} a^{2} - \frac{4017755119}{54} a + \frac{2042488003}{81} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 7 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -16 a^{3} + 16 a^{2} + 112 a - 34\) , \( -86 a^{3} + 86 a^{2} + 602 a - 206\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-1\right){x}^{2}+\left(-16a^{3}+16a^{2}+112a-34\right){x}-86a^{3}+86a^{2}+602a-206$ |
| 6.1-b2 |
6.1-b |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{8} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.079514718$ |
$595.0714443$ |
1.655663451 |
\( \frac{11767}{12} a^{3} - \frac{11767}{12} a^{2} - \frac{82369}{12} a + \frac{47491}{9} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 7 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a + 1\) , \( -2 a^{3} + 2 a^{2} + 14 a - 6\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-1\right){x}^{2}+\left(-a^{3}+a^{2}+7a+1\right){x}-2a^{3}+2a^{2}+14a-6$ |
| 6.1-b3 |
6.1-b |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.079514718$ |
$595.0714443$ |
1.655663451 |
\( \frac{34451}{768} a^{3} - \frac{34451}{768} a^{2} - \frac{241157}{768} a + \frac{10651}{96} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - a^{2} - 7 a + 4\) , \( -3 a^{3} + 3 a^{2} + 21 a + 12\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+{x}^{2}+\left(a^{3}-a^{2}-7a+4\right){x}-3a^{3}+3a^{2}+21a+12$ |
| 6.1-b4 |
6.1-b |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.159029436$ |
$595.0714443$ |
1.655663451 |
\( \frac{54205374865165069}{3} a^{3} + \frac{70270605789877749}{2} a^{2} + \frac{2612326848585175}{2} a - \frac{29174571749575829}{6} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -2 a^{3} + 3 a^{2} + 10 a - 2\) , \( a + 1\) , \( 76 a^{3} - 152 a^{2} - 260 a - 77\) , \( -552 a^{3} + 1306 a^{2} + 1267 a + 210\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+10a-2\right){x}^{2}+\left(76a^{3}-152a^{2}-260a-77\right){x}-552a^{3}+1306a^{2}+1267a+210$ |
| 6.1-b5 |
6.1-b |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{4} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.159029436$ |
$148.7678610$ |
1.655663451 |
\( -\frac{1547627}{2} a^{3} + \frac{1547627}{2} a^{2} + \frac{10833389}{2} a + \frac{7829167}{3} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{2} + 3 a + 4\) , \( a\) , \( -110 a^{3} + 305 a^{2} + 108 a - 47\) , \( 4406 a^{3} - 12448 a^{2} - 3727 a + 2425\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3a+4\right){x}^{2}+\left(-110a^{3}+305a^{2}+108a-47\right){x}+4406a^{3}-12448a^{2}-3727a+2425$ |
| 6.1-b6 |
6.1-b |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.159029436$ |
$595.0714443$ |
1.655663451 |
\( -\frac{488762023013849869}{3} a^{3} + \frac{219433826309245451}{2} a^{2} + \frac{2025318697845277225}{2} a + \frac{2972095626608234357}{6} \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( -120 a^{3} + 196 a^{2} + 567 a - 337\) , \( 1290 a^{3} - 2044 a^{2} - 6434 a + 2892\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+1\right){x}^{2}+\left(-120a^{3}+196a^{2}+567a-337\right){x}+1290a^{3}-2044a^{2}-6434a+2892$ |
| 6.1-b7 |
6.1-b |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.079514718$ |
$2380.285777$ |
1.655663451 |
\( -\frac{1814298623}{12} a^{3} + \frac{1814298623}{12} a^{2} + \frac{12700090361}{12} a + \frac{1663895809}{3} \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( -150 a^{3} + 221 a^{2} + 747 a - 272\) , \( 1299 a^{3} - 1958 a^{2} - 6605 a + 2344\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+1\right){x}^{2}+\left(-150a^{3}+221a^{2}+747a-272\right){x}+1299a^{3}-1958a^{2}-6605a+2344$ |
| 6.1-b8 |
6.1-b |
$8$ |
$16$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$12.77945$ |
$(a+1), (2a^3-3a^2-10a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.039757359$ |
$2380.285777$ |
1.655663451 |
\( -\frac{65471}{16} a^{3} + \frac{65471}{16} a^{2} + \frac{458297}{16} a + \frac{127585}{6} \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( -10 a^{3} + 16 a^{2} + 47 a - 17\) , \( 14 a^{3} - 22 a^{2} - 70 a + 24\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+1\right){x}^{2}+\left(-10a^{3}+16a^{2}+47a-17\right){x}+14a^{3}-22a^{2}-70a+24$ |
| 8.1-a1 |
8.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{14} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2005.666846$ |
2.924172458 |
\( -\frac{28006803}{16} a^{3} + \frac{28006803}{16} a^{2} + \frac{196047621}{16} a + \frac{94432041}{16} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 0\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 5 a^{3} - 5 a^{2} - 35 a - 12\) , \( -7 a^{3} + 7 a^{2} + 49 a + 24\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(5a^{3}-5a^{2}-35a-12\right){x}-7a^{3}+7a^{2}+49a+24$ |
| 8.1-a2 |
8.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{14} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$55.71296795$ |
2.924172458 |
\( \frac{28006803}{16} a^{3} - \frac{28006803}{16} a^{2} - \frac{196047621}{16} a + \frac{33212619}{8} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 0\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -3 a^{3} + 3 a^{2} + 21 a - 8\) , \( -11 a^{3} + 11 a^{2} + 77 a - 28\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-2\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(-3a^{3}+3a^{2}+21a-8\right){x}-11a^{3}+11a^{2}+77a-28$ |
| 8.1-a3 |
8.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{26} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$501.4167115$ |
2.924172458 |
\( \frac{1257201}{4096} a^{3} - \frac{1257201}{4096} a^{2} - \frac{8800407}{4096} a + \frac{713961}{512} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 26 a^{3} - 78 a^{2} - 10 a + 21\) , \( -111 a^{3} + 309 a^{2} + 105 a - 54\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+2\right){x}^{2}+\left(26a^{3}-78a^{2}-10a+21\right){x}-111a^{3}+309a^{2}+105a-54$ |
| 8.1-a4 |
8.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{16} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$222.8518718$ |
2.924172458 |
\( -\frac{26704161}{64} a^{3} + \frac{26704161}{64} a^{2} + \frac{186929127}{64} a + \frac{90308601}{64} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 320 a^{3} - 908 a^{2} - 260 a + 181\) , \( 6179 a^{3} - 17453 a^{2} - 5237 a + 3392\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+2\right){x}^{2}+\left(320a^{3}-908a^{2}-260a+181\right){x}+6179a^{3}-17453a^{2}-5237a+3392$ |
| 8.1-a5 |
8.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$55.71296795$ |
2.924172458 |
\( -\frac{8022622470093}{8} a^{3} + \frac{8022622470093}{8} a^{2} + \frac{56158357290651}{8} a + \frac{27054540068985}{8} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 1790 a^{3} - 5058 a^{2} - 1510 a + 981\) , \( -101387 a^{3} + 286329 a^{2} + 86037 a - 55592\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+2\right){x}^{2}+\left(1790a^{3}-5058a^{2}-1510a+981\right){x}-101387a^{3}+286329a^{2}+86037a-55592$ |
| 8.1-a6 |
8.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$501.4167115$ |
2.924172458 |
\( \frac{8022622470093}{8} a^{3} - \frac{8022622470093}{8} a^{2} - \frac{56158357290651}{8} a + \frac{4757979399723}{2} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -45 a^{3} - 42 a^{2} + 31 a - 78\) , \( -446 a^{3} - 1388 a^{2} - 938 a + 200\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-45a^{3}-42a^{2}+31a-78\right){x}-446a^{3}-1388a^{2}-938a+200$ |
| 8.1-a7 |
8.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{16} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2005.666846$ |
2.924172458 |
\( \frac{26704161}{64} a^{3} - \frac{26704161}{64} a^{2} - \frac{186929127}{64} a + \frac{7950555}{8} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -5 a^{3} - 12 a^{2} - 9 a - 8\) , \( 18 a^{3} + 36 a^{2} + 6 a\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a^{3}-12a^{2}-9a-8\right){x}+18a^{3}+36a^{2}+6a$ |
| 8.1-a8 |
8.1-a |
$8$ |
$12$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{26} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$222.8518718$ |
2.924172458 |
\( -\frac{1257201}{4096} a^{3} + \frac{1257201}{4096} a^{2} + \frac{8800407}{4096} a + \frac{6968889}{4096} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 3 a^{3} - 6 a^{2} - 17 a + 6\) , \( -6 a^{3} + 4 a^{2} + 22 a - 10\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a^{3}-6a^{2}-17a+6\right){x}-6a^{3}+4a^{2}+22a-10$ |
| 8.1-b1 |
8.1-b |
$6$ |
$18$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.225529450$ |
$1212.357383$ |
1.594549854 |
\( \frac{286425}{64} a^{3} - \frac{286425}{64} a^{2} - \frac{2004975}{64} a + 10628 \) |
\( \bigl[a^{2} - 2 a - 2\) , \( -a - 1\) , \( a^{3} - a^{2} - 6 a - 1\) , \( 107 a^{3} - 300 a^{2} - 95 a + 56\) , \( -1259 a^{3} + 3556 a^{2} + 1067 a - 692\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+\left(a^{3}-a^{2}-6a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(107a^{3}-300a^{2}-95a+56\right){x}-1259a^{3}+3556a^{2}+1067a-692$ |
| 8.1-b2 |
8.1-b |
$6$ |
$18$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{54} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.676588352$ |
$14.96737510$ |
1.594549854 |
\( \frac{5519537297}{262144} a^{3} - \frac{5519537297}{262144} a^{2} - \frac{38636761079}{262144} a + \frac{1636371017}{32768} \) |
\( \bigl[a^{2} - 2 a - 2\) , \( -a - 1\) , \( a^{3} - a^{2} - 6 a - 1\) , \( 1277 a^{3} - 3605 a^{2} - 1085 a + 696\) , \( 66818 a^{3} - 188697 a^{2} - 56715 a + 36628\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+\left(a^{3}-a^{2}-6a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1277a^{3}-3605a^{2}-1085a+696\right){x}+66818a^{3}-188697a^{2}-56715a+36628$ |
*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.
