| 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 |
$4$ |
$6$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.339152988$ |
$2231.956118$ |
2.146066534 |
\( 12157674048 a^{3} + 26446888800 a^{2} - 15415344576 a - 33533245728 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 3 a - 1\) , \( a^{3} - 3 a\) , \( -6 a^{3} - 14 a^{2} + 8 a + 19\) , \( 14 a^{3} + 29 a^{2} - 18 a - 38\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(-6a^{3}-14a^{2}+8a+19\right){x}+14a^{3}+29a^{2}-18a-38$ |
| 4.1-a2 |
4.1-a |
$4$ |
$6$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1.017458964$ |
$247.9951242$ |
2.146066534 |
\( -12157674048 a^{3} + 26446888800 a^{2} + 15415344576 a - 33533245728 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a\) , \( 5 a^{3} - 14 a^{2} - 7 a + 19\) , \( 14 a^{3} - 30 a^{2} - 18 a + 38\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(5a^{3}-14a^{2}-7a+19\right){x}+14a^{3}-30a^{2}-18a+38$ |
| 4.1-a3 |
4.1-a |
$4$ |
$6$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.678305976$ |
$1115.978059$ |
2.146066534 |
\( 1291762944 a^{3} - 1454661504 a^{2} - 6112786176 a + 6883318656 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + 5 a^{2} + 6 a - 19\) , \( 2 a^{3} - a^{2} - 9 a + 5\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-a^{3}+5a^{2}+6a-19\right){x}+2a^{3}-a^{2}-9a+5$ |
| 4.1-a4 |
4.1-a |
$4$ |
$6$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$2.034917928$ |
$123.9975621$ |
2.146066534 |
\( -1291762944 a^{3} - 1454661504 a^{2} + 6112786176 a + 6883318656 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - 3 a\) , \( a^{2} - 2\) , \( 3 a^{3} + 3 a^{2} - 14 a - 10\) , \( 4 a^{3} + 4 a^{2} - 18 a - 19\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(3a^{3}+3a^{2}-14a-10\right){x}+4a^{3}+4a^{2}-18a-19$ |
| 4.1-b1 |
4.1-b |
$8$ |
$12$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 1 \) |
$2.579744927$ |
$417.4855389$ |
2.290030940 |
\( 54000 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{2} - 2\) , \( -49 a^{3} + 53 a^{2} + 232 a - 252\) , \( -280 a^{3} + 311 a^{2} + 1322 a - 1480\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-4\right){x}^{2}+\left(-49a^{3}+53a^{2}+232a-252\right){x}-280a^{3}+311a^{2}+1322a-1480$ |
| 4.1-b2 |
4.1-b |
$8$ |
$12$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 3 \) |
$0.859914975$ |
$3757.369850$ |
2.290030940 |
\( 54000 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a^{2} - 2\) , \( 87 a^{3} - 199 a^{2} - 102 a + 264\) , \( -1342 a^{3} + 2911 a^{2} + 1710 a - 3682\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+2\right){x}^{2}+\left(87a^{3}-199a^{2}-102a+264\right){x}-1342a^{3}+2911a^{2}+1710a-3682$ |
| 4.1-b3 |
4.1-b |
$8$ |
$12$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.289872463$ |
$208.7427694$ |
2.290030940 |
\( 818626500 a^{2} - 1037974500 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{2} - 3\) , \( a^{3} - 4 a\) , \( -8 a^{2} + 7\) , \( -42 a^{2} + 51\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-8a^{2}+7\right){x}-42a^{2}+51$ |
| 4.1-b4 |
4.1-b |
$8$ |
$12$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.289872463$ |
$208.7427694$ |
2.290030940 |
\( -818626500 a^{2} + 3873784500 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{2} - 3\) , \( 0\) , \( 2 a^{2} - 5\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(2a^{2}-5\right){x}-1$ |
| 4.1-b5 |
4.1-b |
$8$ |
$12$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1.289872463$ |
$208.7427694$ |
2.290030940 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - 3\) , \( a\) , \( 1\) , \( -1\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+{x}-1$ |
| 4.1-b6 |
4.1-b |
$8$ |
$12$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.429957487$ |
$1878.684925$ |
2.290030940 |
\( 0 \) |
\( \bigl[0\) , \( -a^{2} + 3\) , \( a^{3} - 3 a\) , \( 1\) , \( -a^{2} + 1\bigr] \) |
${y}^2+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+{x}-a^{2}+1$ |
| 4.1-b7 |
4.1-b |
$8$ |
$12$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.429957487$ |
$1878.684925$ |
2.290030940 |
\( -818626500 a^{2} + 3873784500 \) |
\( \bigl[a\) , \( a^{2} - 3\) , \( a^{3} - 4 a\) , \( -a^{2} + 1\) , \( -2 a^{2} + 3\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{2}+1\right){x}-2a^{2}+3$ |
| 4.1-b8 |
4.1-b |
$8$ |
$12$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.429957487$ |
$1878.684925$ |
2.290030940 |
\( 818626500 a^{2} - 1037974500 \) |
\( \bigl[a\) , \( a^{2} - 3\) , \( 0\) , \( -10 a^{2} + 13\) , \( 15 a^{2} - 19\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-10a^{2}+13\right){x}+15a^{2}-19$ |
| 4.1-c1 |
4.1-c |
$4$ |
$6$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.339152988$ |
$2231.956118$ |
2.146066534 |
\( -12157674048 a^{3} + 26446888800 a^{2} + 15415344576 a - 33533245728 \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 3 a\) , \( 5 a^{3} - 14 a^{2} - 8 a + 19\) , \( -14 a^{3} + 29 a^{2} + 18 a - 38\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(5a^{3}-14a^{2}-8a+19\right){x}-14a^{3}+29a^{2}+18a-38$ |
| 4.1-c2 |
4.1-c |
$4$ |
$6$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1.017458964$ |
$247.9951242$ |
2.146066534 |
\( 12157674048 a^{3} + 26446888800 a^{2} - 15415344576 a - 33533245728 \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a\) , \( -6 a^{3} - 14 a^{2} + 9 a + 19\) , \( -14 a^{3} - 30 a^{2} + 18 a + 38\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(-6a^{3}-14a^{2}+9a+19\right){x}-14a^{3}-30a^{2}+18a+38$ |
| 4.1-c3 |
4.1-c |
$4$ |
$6$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.678305976$ |
$1115.978059$ |
2.146066534 |
\( -1291762944 a^{3} - 1454661504 a^{2} + 6112786176 a + 6883318656 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + 5 a^{2} - 8 a - 19\) , \( -2 a^{3} - a^{2} + 7 a + 5\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(a^{3}+5a^{2}-8a-19\right){x}-2a^{3}-a^{2}+7a+5$ |
| 4.1-c4 |
4.1-c |
$4$ |
$6$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.49433$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$2.034917928$ |
$123.9975621$ |
2.146066534 |
\( 1291762944 a^{3} - 1454661504 a^{2} - 6112786176 a + 6883318656 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + 3 a\) , \( a^{2} - 2\) , \( -3 a^{3} + 3 a^{2} + 12 a - 10\) , \( -4 a^{3} + 4 a^{2} + 18 a - 19\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(-3a^{3}+3a^{2}+12a-10\right){x}-4a^{3}+4a^{2}+18a-19$ |
| 6.1-a1 |
6.1-a |
$2$ |
$5$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{5} \) |
$13.14390$ |
$(a-2), (a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$105.8462225$ |
0.900240404 |
\( -\frac{1449121}{36} a^{3} - \frac{493450}{3} a^{2} + \frac{1431181}{6} a - \frac{11141}{6} \) |
\( \bigl[1\) , \( a^{3} - 5 a + 1\) , \( a\) , \( -17 a^{3} + 10 a^{2} + 71 a - 66\) , \( -86 a^{3} + 115 a^{2} + 426 a - 504\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-17a^{3}+10a^{2}+71a-66\right){x}-86a^{3}+115a^{2}+426a-504$ |
| 6.1-a2 |
6.1-a |
$2$ |
$5$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3 \) |
$13.14390$ |
$(a-2), (a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$105.8462225$ |
0.900240404 |
\( -\frac{56375720829614840558952975005}{6} a^{3} - 20439278297811289017906884375 a^{2} + 11913591616438760016673171884 a + 25915966411584796256587875739 \) |
\( \bigl[1\) , \( -a^{3} + 5 a + 1\) , \( 0\) , \( -765 a^{3} + 2310 a^{2} + 290 a - 3690\) , \( -27896 a^{3} + 52051 a^{2} + 44429 a - 55800\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-765a^{3}+2310a^{2}+290a-3690\right){x}-27896a^{3}+52051a^{2}+44429a-55800$ |
| 6.1-b1 |
6.1-b |
$2$ |
$5$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{5} \) |
$13.14390$ |
$(a-2), (a^2+a-3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$349.5585792$ |
2.973056091 |
\( \frac{1449121}{36} a^{3} - \frac{493450}{3} a^{2} - \frac{1431181}{6} a - \frac{11141}{6} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 19 a^{3} + 10 a^{2} - 83 a - 67\) , \( -68 a^{3} - 106 a^{2} + 348 a + 437\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(19a^{3}+10a^{2}-83a-67\right){x}-68a^{3}-106a^{2}+348a+437$ |
| 6.1-b2 |
6.1-b |
$2$ |
$5$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3 \) |
$13.14390$ |
$(a-2), (a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.559293726$ |
2.973056091 |
\( \frac{56375720829614840558952975005}{6} a^{3} - 20439278297811289017906884375 a^{2} - 11913591616438760016673171884 a + 25915966411584796256587875739 \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a + 1\) , \( a^{2} - 3\) , \( 763 a^{3} + 2310 a^{2} - 280 a - 3691\) , \( -27132 a^{3} - 49741 a^{2} + 44144 a + 52109\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(763a^{3}+2310a^{2}-280a-3691\right){x}-27132a^{3}-49741a^{2}+44144a+52109$ |
| 6.1-c1 |
6.1-c |
$2$ |
$5$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{5} \) |
$13.14390$ |
$(a-2), (a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$105.8462225$ |
0.900240404 |
\( \frac{1449121}{36} a^{3} - \frac{493450}{3} a^{2} - \frac{1431181}{6} a - \frac{11141}{6} \) |
\( \bigl[1\) , \( -a^{3} + 5 a + 1\) , \( a\) , \( 17 a^{3} + 10 a^{2} - 72 a - 66\) , \( 86 a^{3} + 115 a^{2} - 426 a - 504\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(17a^{3}+10a^{2}-72a-66\right){x}+86a^{3}+115a^{2}-426a-504$ |
| 6.1-c2 |
6.1-c |
$2$ |
$5$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3 \) |
$13.14390$ |
$(a-2), (a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$105.8462225$ |
0.900240404 |
\( \frac{56375720829614840558952975005}{6} a^{3} - 20439278297811289017906884375 a^{2} - 11913591616438760016673171884 a + 25915966411584796256587875739 \) |
\( \bigl[1\) , \( a^{3} - 5 a + 1\) , \( 0\) , \( 765 a^{3} + 2310 a^{2} - 290 a - 3690\) , \( 27896 a^{3} + 52051 a^{2} - 44429 a - 55800\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(765a^{3}+2310a^{2}-290a-3690\right){x}+27896a^{3}+52051a^{2}-44429a-55800$ |
| 6.1-d1 |
6.1-d |
$2$ |
$5$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{5} \) |
$13.14390$ |
$(a-2), (a^2+a-3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$349.5585792$ |
2.973056091 |
\( -\frac{1449121}{36} a^{3} - \frac{493450}{3} a^{2} + \frac{1431181}{6} a - \frac{11141}{6} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -19 a^{3} + 10 a^{2} + 80 a - 67\) , \( 68 a^{3} - 106 a^{2} - 351 a + 437\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-19a^{3}+10a^{2}+80a-67\right){x}+68a^{3}-106a^{2}-351a+437$ |
| 6.1-d2 |
6.1-d |
$2$ |
$5$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3 \) |
$13.14390$ |
$(a-2), (a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.559293726$ |
2.973056091 |
\( -\frac{56375720829614840558952975005}{6} a^{3} - 20439278297811289017906884375 a^{2} + 11913591616438760016673171884 a + 25915966411584796256587875739 \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 5 a + 1\) , \( a^{2} - 3\) , \( -763 a^{3} + 2310 a^{2} + 280 a - 3691\) , \( 27132 a^{3} - 49741 a^{2} - 44144 a + 52109\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-763a^{3}+2310a^{2}+280a-3691\right){x}+27132a^{3}-49741a^{2}-44144a+52109$ |
| 8.1-a1 |
8.1-a |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.62516$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$284.7066550$ |
2.421479274 |
\( 77056 a^{3} + 167808 a^{2} - 98560 a - 213376 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 27 a^{3} + 29 a^{2} - 128 a - 139\) , \( 246 a^{3} + 278 a^{2} - 1165 a - 1318\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-4\right){x}^{2}+\left(27a^{3}+29a^{2}-128a-139\right){x}+246a^{3}+278a^{2}-1165a-1318$ |
| 8.1-a2 |
8.1-a |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$13.62516$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$569.4133100$ |
2.421479274 |
\( -643008 a^{3} - 702304 a^{2} + 3018688 a + 3377696 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 4\) , \( a\) , \( 4 a^{3} - 5 a^{2} - 8 a + 15\) , \( 5 a^{3} - 4 a^{2} - 10 a + 5\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-3a+4\right){x}^{2}+\left(4a^{3}-5a^{2}-8a+15\right){x}+5a^{3}-4a^{2}-10a+5$ |
| 8.1-b1 |
8.1-b |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.62516$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$284.7066550$ |
2.421479274 |
\( -77056 a^{3} + 167808 a^{2} + 98560 a - 213376 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -27 a^{3} + 29 a^{2} + 126 a - 139\) , \( -246 a^{3} + 278 a^{2} + 1163 a - 1318\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(-27a^{3}+29a^{2}+126a-139\right){x}-246a^{3}+278a^{2}+1163a-1318$ |
| 8.1-b2 |
8.1-b |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$13.62516$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$569.4133100$ |
2.421479274 |
\( 643008 a^{3} - 702304 a^{2} - 3018688 a + 3377696 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} - 3 a\) , \( -7 a^{3} - 9 a^{2} + 22 a + 21\) , \( -12 a^{3} - 22 a^{2} + 28 a + 38\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+4\right){x}^{2}+\left(-7a^{3}-9a^{2}+22a+21\right){x}-12a^{3}-22a^{2}+28a+38$ |
| 8.1-c1 |
8.1-c |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.62516$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.054653259$ |
$1952.971958$ |
1.815621053 |
\( -77056 a^{3} + 167808 a^{2} + 98560 a - 213376 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + 5 a + 1\) , \( a^{2} - 2\) , \( -29 a^{3} + 27 a^{2} + 136 a - 128\) , \( 218 a^{3} - 251 a^{2} - 1032 a + 1185\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-29a^{3}+27a^{2}+136a-128\right){x}+218a^{3}-251a^{2}-1032a+1185$ |
| 8.1-c2 |
8.1-c |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$13.62516$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.027326629$ |
$3905.943917$ |
1.815621053 |
\( 643008 a^{3} - 702304 a^{2} - 3018688 a + 3377696 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - 3 a\) , \( -a^{3} + a - 5\) , \( -a^{2} + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-a^{3}+a-5\right){x}-a^{2}+1$ |
| 8.1-d1 |
8.1-d |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.62516$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.054653259$ |
$1952.971958$ |
1.815621053 |
\( 77056 a^{3} + 167808 a^{2} - 98560 a - 213376 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - 5 a + 1\) , \( a^{2} - 2\) , \( 29 a^{3} + 27 a^{2} - 138 a - 128\) , \( -218 a^{3} - 251 a^{2} + 1032 a + 1185\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(29a^{3}+27a^{2}-138a-128\right){x}-218a^{3}-251a^{2}+1032a+1185$ |
| 8.1-d2 |
8.1-d |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$13.62516$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.027326629$ |
$3905.943917$ |
1.815621053 |
\( -643008 a^{3} - 702304 a^{2} + 3018688 a + 3377696 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a\) , \( 2 a^{3} - 6 a^{2} - a + 13\) , \( -3 a^{3} + 7 a^{2} + 4 a - 8\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(2a^{3}-6a^{2}-a+13\right){x}-3a^{3}+7a^{2}+4a-8$ |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$13.82725$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.424653516$ |
$321.8651414$ |
2.324993817 |
\( \frac{6082816}{3} a^{2} - \frac{7712704}{3} \) |
\( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -5 a^{3} - 2 a^{2} + 15 a - 9\) , \( -251 a^{3} + 294 a^{2} + 1198 a - 1369\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a^{3}-2a^{2}+15a-9\right){x}-251a^{3}+294a^{2}+1198a-1369$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$13.82725$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.212326758$ |
$321.8651414$ |
2.324993817 |
\( -\frac{199424}{9} a^{2} + \frac{925888}{9} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 13 a^{3} - 11 a^{2} - 36 a - 6\) , \( 37 a^{3} - 104 a^{2} - 23 a + 158\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(13a^{3}-11a^{2}-36a-6\right){x}+37a^{3}-104a^{2}-23a+158$ |
| 9.1-b1 |
9.1-b |
$6$ |
$18$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.82725$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$4.109456483$ |
$32.34405507$ |
2.260955354 |
\( 44330496 a^{2} - 56220480 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 4 a - 4\) , \( a^{2} + a - 3\) , \( 157 a^{3} - 334 a^{2} - 206 a + 420\) , \( 2844 a^{3} - 6181 a^{2} - 3609 a + 7832\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-4\right){x}^{2}+\left(157a^{3}-334a^{2}-206a+420\right){x}+2844a^{3}-6181a^{2}-3609a+7832$ |
| 9.1-b2 |
9.1-b |
$6$ |
$18$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.82725$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$2.054728241$ |
$32.34405507$ |
2.260955354 |
\( -44330496 a^{2} + 209762496 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - 3 a + 1\) , \( 88 a^{3} + 92 a^{2} - 406 a - 452\) , \( 794 a^{3} + 873 a^{2} - 3732 a - 4179\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-4\right){x}^{2}+\left(88a^{3}+92a^{2}-406a-452\right){x}+794a^{3}+873a^{2}-3732a-4179$ |
| 9.1-b3 |
9.1-b |
$6$ |
$18$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.82725$ |
$(a^2+a-3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.456606275$ |
$2619.868460$ |
2.260955354 |
\( 44330496 a^{2} - 56220480 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 153 a^{3} - 338 a^{2} - 192 a + 432\) , \( -3025 a^{3} + 6577 a^{2} + 3837 a - 8338\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+2\right){x}^{2}+\left(153a^{3}-338a^{2}-192a+432\right){x}-3025a^{3}+6577a^{2}+3837a-8338$ |
| 9.1-b4 |
9.1-b |
$6$ |
$18$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.82725$ |
$(a^2+a-3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.228303137$ |
$2619.868460$ |
2.260955354 |
\( -44330496 a^{2} + 209762496 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a + 1\) , \( 84 a^{3} + 86 a^{2} - 390 a - 428\) , \( -618 a^{3} - 664 a^{2} + 2890 a + 3215\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+2\right){x}^{2}+\left(84a^{3}+86a^{2}-390a-428\right){x}-618a^{3}-664a^{2}+2890a+3215$ |
| 9.1-b5 |
9.1-b |
$6$ |
$18$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.82725$ |
$(a^2+a-3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1.369818827$ |
$873.2894869$ |
2.260955354 |
\( 1728 \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( 1\) , \( -a^{2} + 4\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-a^{2}+4\right){x}-1$ |
| 9.1-b6 |
9.1-b |
$6$ |
$18$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.82725$ |
$(a^2+a-3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$0.684909413$ |
$873.2894869$ |
2.260955354 |
\( 1728 \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}$ |
| 9.1-c1 |
9.1-c |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$13.82725$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.212326758$ |
$321.8651414$ |
2.324993817 |
\( -\frac{199424}{9} a^{2} + \frac{925888}{9} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 4 a - 1\) , \( a^{3} - 4 a + 1\) , \( 13 a^{3} - 11 a^{2} - 36 a - 5\) , \( -37 a^{3} + 105 a^{2} + 22 a - 165\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(13a^{3}-11a^{2}-36a-5\right){x}-37a^{3}+105a^{2}+22a-165$ |
| 9.1-c2 |
9.1-c |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$13.82725$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.424653516$ |
$321.8651414$ |
2.324993817 |
\( \frac{6082816}{3} a^{2} - \frac{7712704}{3} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 2\) , \( a^{3} - 4 a + 1\) , \( -5 a^{3} - 2 a^{2} + 15 a - 8\) , \( 251 a^{3} - 293 a^{2} - 1199 a + 1362\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-5a^{3}-2a^{2}+15a-8\right){x}+251a^{3}-293a^{2}-1199a+1362$ |
| 12.1-a1 |
12.1-a |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$14.33353$ |
$(a-2), (a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$281.3841477$ |
2.393220776 |
\( -\frac{31739840}{3} a^{3} + 22910944 a^{2} + \frac{40586944}{3} a - \frac{86756704}{3} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 5 a\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -58 a^{3} + 20 a^{2} + 228 a - 194\) , \( 160 a^{3} - 434 a^{2} - 1023 a + 1475\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-58a^{3}+20a^{2}+228a-194\right){x}+160a^{3}-434a^{2}-1023a+1475$ |
| 12.1-a2 |
12.1-a |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$14.33353$ |
$(a-2), (a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$140.6920738$ |
2.393220776 |
\( \frac{57088}{9} a^{3} - \frac{76160}{9} a^{2} - \frac{245504}{9} a + \frac{307072}{9} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 3 a + 4\) , \( a^{2} - 2\) , \( 15 a^{3} + 2 a^{2} - 60 a - 31\) , \( 17 a^{3} - 5 a^{2} - 59 a - 23\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+4\right){x}^{2}+\left(15a^{3}+2a^{2}-60a-31\right){x}+17a^{3}-5a^{2}-59a-23$ |
| 12.1-b1 |
12.1-b |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$14.33353$ |
$(a-2), (a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$281.3841477$ |
2.393220776 |
\( \frac{31739840}{3} a^{3} + 22910944 a^{2} - \frac{40586944}{3} a - \frac{86756704}{3} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 5 a\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 57 a^{3} + 20 a^{2} - 228 a - 194\) , \( -161 a^{3} - 434 a^{2} + 1023 a + 1475\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(57a^{3}+20a^{2}-228a-194\right){x}-161a^{3}-434a^{2}+1023a+1475$ |
| 12.1-b2 |
12.1-b |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$14.33353$ |
$(a-2), (a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$140.6920738$ |
2.393220776 |
\( -\frac{57088}{9} a^{3} - \frac{76160}{9} a^{2} + \frac{245504}{9} a + \frac{307072}{9} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( a^{2} - 2\) , \( -15 a^{3} + 2 a^{2} + 58 a - 31\) , \( -17 a^{3} - 5 a^{2} + 59 a - 23\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+4\right){x}^{2}+\left(-15a^{3}+2a^{2}+58a-31\right){x}-17a^{3}-5a^{2}+59a-23$ |
| 12.1-c1 |
12.1-c |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$14.33353$ |
$(a-2), (a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.019665283$ |
$2234.949414$ |
2.242860625 |
\( \frac{31739840}{3} a^{3} + 22910944 a^{2} - \frac{40586944}{3} a - \frac{86756704}{3} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 5 a + 4\) , \( a\) , \( 55 a^{3} + 20 a^{2} - 217 a - 191\) , \( 217 a^{3} + 453 a^{2} - 1246 a - 1668\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}-a^{2}+5a+4\right){x}^{2}+\left(55a^{3}+20a^{2}-217a-191\right){x}+217a^{3}+453a^{2}-1246a-1668$ |
| 12.1-c2 |
12.1-c |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$14.33353$ |
$(a-2), (a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.039330566$ |
$1117.474707$ |
2.242860625 |
\( -\frac{57088}{9} a^{3} - \frac{76160}{9} a^{2} + \frac{245504}{9} a + \frac{307072}{9} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 2\) , \( -13 a^{3} + 4 a^{2} + 46 a - 39\) , \( -8 a^{3} + 36 a^{2} + 69 a - 112\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-13a^{3}+4a^{2}+46a-39\right){x}-8a^{3}+36a^{2}+69a-112$ |
| 12.1-d1 |
12.1-d |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$14.33353$ |
$(a-2), (a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.019665283$ |
$2234.949414$ |
2.242860625 |
\( -\frac{31739840}{3} a^{3} + 22910944 a^{2} + \frac{40586944}{3} a - \frac{86756704}{3} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 5 a + 4\) , \( a\) , \( -56 a^{3} + 20 a^{2} + 219 a - 191\) , \( -217 a^{3} + 453 a^{2} + 1246 a - 1668\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-5a+4\right){x}^{2}+\left(-56a^{3}+20a^{2}+219a-191\right){x}-217a^{3}+453a^{2}+1246a-1668$ |
| 12.1-d2 |
12.1-d |
$2$ |
$2$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$14.33353$ |
$(a-2), (a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.039330566$ |
$1117.474707$ |
2.242860625 |
\( \frac{57088}{9} a^{3} - \frac{76160}{9} a^{2} - \frac{245504}{9} a + \frac{307072}{9} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{2} - 2\) , \( 13 a^{3} + 4 a^{2} - 48 a - 39\) , \( 8 a^{3} + 36 a^{2} - 69 a - 112\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(13a^{3}+4a^{2}-48a-39\right){x}+8a^{3}+36a^{2}-69a-112$ |
*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.
