| 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 |
| 3.1-a1 |
3.1-a |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$3.38169$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.331020862$ |
$28.79466320$ |
1.81486362 |
\( -\frac{1675}{3} a^{2} - \frac{256}{3} a - \frac{736}{3} \) |
\( \bigl[a^{2} + a - 4\) , \( 1\) , \( a^{2} - 4\) , \( 3 a^{2} + 4 a - 5\) , \( 4 a^{2} + 6 a - 7\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+{x}^{2}+\left(3a^{2}+4a-5\right){x}+4a^{2}+6a-7$ |
| 3.2-a1 |
3.2-a |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{3} \) |
$3.38169$ |
$(-a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$191.1971301$ |
2.02248584 |
\( -\frac{4360585216}{27} a^{2} - \frac{2577657856}{9} a + \frac{1572290560}{9} \) |
\( \bigl[0\) , \( a^{2} + a - 4\) , \( a\) , \( -91 a^{2} - 160 a + 102\) , \( 949 a^{2} + 1682 a - 1030\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-91a^{2}-160a+102\right){x}+949a^{2}+1682a-1030$ |
| 3.2-a2 |
3.2-a |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( -3 \) |
$3.38169$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$63.73237672$ |
2.02248584 |
\( \frac{1581056}{3} a^{2} - 274432 a - 3293184 \) |
\( \bigl[0\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( -10 a^{2} - 15 a + 17\) , \( 76 a^{2} + 135 a - 82\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-10a^{2}-15a+17\right){x}+76a^{2}+135a-82$ |
| 7.1-a1 |
7.1-a |
$3$ |
$9$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$3.89460$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$32.87362748$ |
2.08642607 |
\( -\frac{391389}{49} a^{2} + \frac{1309689}{49} a - \frac{542074}{49} \) |
\( \bigl[a^{2} + a - 4\) , \( -a + 1\) , \( 1\) , \( a^{2} + 6 a + 2\) , \( a^{2} + 12 a - 5\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a^{2}+6a+2\right){x}+a^{2}+12a-5$ |
| 7.1-a2 |
7.1-a |
$3$ |
$9$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$3.89460$ |
$(-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$295.8626474$ |
2.08642607 |
\( -\frac{1388306177170}{49} a^{2} - \frac{2462032939535}{49} a + \frac{1501680516593}{49} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 5\) , \( a^{2} + a - 3\) , \( 30 a^{2} - 29 a - 214\) , \( -131 a^{2} + 89 a + 867\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(30a^{2}-29a-214\right){x}-131a^{2}+89a+867$ |
| 7.1-a3 |
7.1-a |
$3$ |
$9$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{6} \) |
$3.89460$ |
$(-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$98.62088246$ |
2.08642607 |
\( -\frac{56693265}{117649} a^{2} - \frac{135751170}{117649} a + \frac{86549543}{117649} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} + a - 3\) , \( -a^{2} - 2 a + 2\) , \( -a^{2} - 2 a\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a^{2}-2a+2\right){x}-a^{2}-2a$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$3.98225$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$1$ |
$15.38539779$ |
1.46472252 |
\( -\frac{418003673}{8} a^{2} + \frac{94407933}{2} a + \frac{2167828053}{8} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( a^{2} + a - 3\) , \( -15 a^{2} + 60 a - 34\) , \( -126 a^{2} + 423 a - 179\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-15a^{2}+60a-34\right){x}-126a^{2}+423a-179$ |
| 9.1-a1 |
9.1-a |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$4.06119$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$43.30152483$ |
2.74826471 |
\( -\frac{1675}{3} a^{2} - \frac{256}{3} a - \frac{736}{3} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a\) , \( -3 a^{2} - 4 a + 9\) , \( -3 a^{2} - 4 a + 5\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-3a^{2}-4a+9\right){x}-3a^{2}-4a+5$ |
| 9.2-a1 |
9.2-a |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$4.06119$ |
$(-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 5 \) |
$1$ |
$7.023669804$ |
2.22889424 |
\( -\frac{297608752174531490}{81} a^{2} + \frac{51582478664336465}{27} a + \frac{619978673975480117}{27} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 4\) , \( 8 a^{2} - 17 a - 76\) , \( 58 a^{2} - 67 a - 424\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(8a^{2}-17a-76\right){x}+58a^{2}-67a-424$ |
| 9.2-a2 |
9.2-a |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{21} \) |
$4.06119$ |
$(-a), (-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$56.18935843$ |
2.22889424 |
\( \frac{1722643277906}{59049} a^{2} - \frac{69099627659}{729} a + \frac{2290589613193}{59049} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 4\) , \( -12 a^{2} + 13 a - 6\) , \( 32 a^{2} - 73 a + 16\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-12a^{2}+13a-6\right){x}+32a^{2}-73a+16$ |
| 9.2-a3 |
9.2-a |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{12} \) |
$4.06119$ |
$(-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$56.18935843$ |
2.22889424 |
\( -\frac{5882577625}{243} a^{2} + \frac{1019279950}{81} a + \frac{36766736779}{243} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 4\) , \( -2 a^{2} - 2 a - 1\) , \( a^{2} - 4 a - 10\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-2a^{2}-2a-1\right){x}+a^{2}-4a-10$ |
| 9.2-a4 |
9.2-a |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$4.06119$ |
$(-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$1$ |
$56.18935843$ |
2.22889424 |
\( \frac{61267}{27} a^{2} - \frac{42523}{27} a - 11358 \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 4\) , \( -2 a^{2} - 2 a + 4\) , \( -a^{2} - a + 2\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-2a^{2}-2a+4\right){x}-a^{2}-a+2$ |
| 9.2-b1 |
9.2-b |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{13} \) |
$4.06119$ |
$(-a), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.353438599$ |
$29.29863318$ |
1.97168696 |
\( \frac{40960}{9} a^{2} - \frac{585728}{243} a - \frac{6762496}{243} \) |
\( \bigl[0\) , \( a^{2} - a - 4\) , \( a + 1\) , \( 3 a^{2} - 12 a + 11\) , \( 16 a^{2} - 52 a + 18\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(3a^{2}-12a+11\right){x}+16a^{2}-52a+18$ |
| 9.2-c1 |
9.2-c |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{21} \) |
$4.06119$ |
$(-a), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$21.27731082$ |
1.35043010 |
\( \frac{15750997322227712}{1162261467} a^{2} - \frac{2729975418155008}{387420489} a - \frac{32812401523920896}{387420489} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 94 a^{2} + 161 a - 114\) , \( -1734 a^{2} - 3069 a + 1889\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(94a^{2}+161a-114\right){x}-1734a^{2}-3069a+1889$ |
| 9.3-a1 |
9.3-a |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{3} \) |
$4.06119$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.074590750$ |
$148.8699425$ |
2.11430980 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - a - 3\) , \( a + 1\) , \( -a + 4\) , \( -8 a^{2} + 3 a + 50\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a+4\right){x}-8a^{2}+3a+50$ |
| 9.3-a2 |
9.3-a |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$4.06119$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.223772251$ |
$49.62331419$ |
2.11430980 |
\( 0 \) |
\( \bigl[0\) , \( -a^{2} + a + 3\) , \( a^{2} - 4\) , \( -a + 4\) , \( 18099 a^{2} - 9411 a - 113115\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-a+4\right){x}+18099a^{2}-9411a-113115$ |
| 9.3-b1 |
9.3-b |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{7} \) |
$4.06119$ |
$(-a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$88.06352971$ |
0.621024810 |
\( \frac{1581056}{3} a^{2} - 274432 a - 3293184 \) |
\( \bigl[0\) , \( a^{2} + a - 5\) , \( a^{2} + a - 4\) , \( a^{2} - 2 a - 8\) , \( -13 a^{2} - 9 a + 45\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(a^{2}-2a-8\right){x}-13a^{2}-9a+45$ |
| 9.3-b2 |
9.3-b |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$4.06119$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$9.784836634$ |
0.621024810 |
\( -\frac{4360585216}{27} a^{2} - \frac{2577657856}{9} a + \frac{1572290560}{9} \) |
\( \bigl[0\) , \( -a^{2} + 4\) , \( a + 1\) , \( -31 a^{2} - 15 a + 124\) , \( -726 a^{2} + 260 a + 4272\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-31a^{2}-15a+124\right){x}-726a^{2}+260a+4272$ |
| 15.1-a1 |
15.1-a |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{3} \cdot 5^{5} \) |
$4.42210$ |
$(-a), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.064217361$ |
$240.3321861$ |
1.46930184 |
\( \frac{868942064}{28125} a^{2} - \frac{304032401}{28125} a - \frac{570155764}{3125} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( 1\) , \( -53 a^{2} + 164 a - 49\) , \( 799 a^{2} - 2604 a + 1076\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-53a^{2}+164a-49\right){x}+799a^{2}-2604a+1076$ |
| 15.1-b1 |
15.1-b |
$4$ |
$6$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5^{3} \) |
$4.42210$ |
$(-a), (a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$402.6995009$ |
1.06494020 |
\( -\frac{147292757}{375} a^{2} - \frac{88412962}{375} a + \frac{187688821}{125} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -12 a^{2} - 20 a + 15\) , \( 65 a^{2} + 115 a - 72\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-12a^{2}-20a+15\right){x}+65a^{2}+115a-72$ |
| 15.1-b2 |
15.1-b |
$4$ |
$6$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{6} \) |
$4.42210$ |
$(-a), (a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$100.6748752$ |
1.06494020 |
\( \frac{19221936686538466}{46875} a^{2} + \frac{34087940492362381}{46875} a - \frac{20792554915248269}{46875} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -187 a^{2} - 330 a + 205\) , \( 3542 a^{2} + 6282 a - 3831\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-187a^{2}-330a+205\right){x}+3542a^{2}+6282a-3831$ |
| 15.1-b3 |
15.1-b |
$4$ |
$6$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{3} \cdot 5 \) |
$4.42210$ |
$(-a), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$134.2331669$ |
1.06494020 |
\( \frac{214801}{45} a^{2} - \frac{802009}{45} a + \frac{63774}{5} \) |
\( \bigl[a + 1\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -a^{2} + a + 8\) , \( 8 a^{2} + 15 a - 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-a^{2}+a+8\right){x}+8a^{2}+15a-8$ |
| 15.1-b4 |
15.1-b |
$4$ |
$6$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{6} \cdot 5^{2} \) |
$4.42210$ |
$(-a), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$33.55829174$ |
1.06494020 |
\( \frac{286801863239}{675} a^{2} - \frac{311027108492}{225} a + \frac{381820335049}{675} \) |
\( \bigl[a + 1\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -26 a^{2} - 39 a + 33\) , \( 137 a^{2} + 249 a - 150\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-26a^{2}-39a+33\right){x}+137a^{2}+249a-150$ |
| 15.1-c1 |
15.1-c |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{17} \cdot 5 \) |
$4.42210$ |
$(-a), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 17 \) |
$0.043344838$ |
$31.98058183$ |
2.24346503 |
\( \frac{61857233}{98415} a^{2} + \frac{337862188}{98415} a - \frac{400078184}{32805} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 3\) , \( a^{2} + a - 4\) , \( -10 a^{2} + 19 a - 13\) , \( 15 a^{2} - 92 a + 38\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-10a^{2}+19a-13\right){x}+15a^{2}-92a+38$ |
| 15.1-d1 |
15.1-d |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{3} \cdot 5^{4} \) |
$4.42210$ |
$(-a), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$5.168428596$ |
$8.437833455$ |
2.07589845 |
\( -\frac{111567286302566458244408}{5625} a^{2} + \frac{58011571801495054889447}{5625} a + \frac{77472338783877222614558}{625} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 5\) , \( a\) , \( -64 a^{2} + 1254 a - 2937\) , \( 16586 a^{2} - 35487 a - 29073\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-64a^{2}+1254a-2937\right){x}+16586a^{2}-35487a-29073$ |
| 15.1-d2 |
15.1-d |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$4.42210$ |
$(-a), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.584214298$ |
$33.75133382$ |
2.07589845 |
\( -\frac{1172344142701}{675} a^{2} + \frac{24982015892}{25} a + \frac{7473014084284}{675} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 5\) , \( a\) , \( -129 a^{2} + 504 a - 357\) , \( -2581 a^{2} + 8688 a - 4161\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-129a^{2}+504a-357\right){x}-2581a^{2}+8688a-4161$ |
| 15.1-d3 |
15.1-d |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{3} \cdot 5 \) |
$4.42210$ |
$(-a), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.292107149$ |
$67.50266764$ |
2.07589845 |
\( \frac{1147466539}{45} a^{2} - \frac{3735692041}{45} a + \frac{170402441}{5} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 5\) , \( a\) , \( -149 a^{2} + 509 a - 217\) , \( -2747 a^{2} + 8975 a - 3680\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-149a^{2}+509a-217\right){x}-2747a^{2}+8975a-3680$ |
| 15.1-d4 |
15.1-d |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{12} \cdot 5 \) |
$4.42210$ |
$(-a), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$5.168428596$ |
$8.437833455$ |
2.07589845 |
\( \frac{73935561967304142616}{3645} a^{2} + \frac{43705464955331103647}{1215} a - \frac{79976812821391253494}{3645} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 5\) , \( a\) , \( 126 a^{2} - 326 a - 17\) , \( -10384 a^{2} + 34075 a - 14553\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(126a^{2}-326a-17\right){x}-10384a^{2}+34075a-14553$ |
| 15.1-e1 |
15.1-e |
$2$ |
$2$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{9} \cdot 5^{7} \) |
$4.42210$ |
$(-a), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 7 \) |
$1$ |
$35.16519306$ |
1.95288393 |
\( \frac{70559388762215893}{18984375} a^{2} - \frac{229560348781095187}{18984375} a + \frac{31313233993434121}{6328125} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 4\) , \( 0\) , \( 11 a^{2} + 13 a - 24\) , \( 2765 a^{2} + 4857 a - 3096\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(11a^{2}+13a-24\right){x}+2765a^{2}+4857a-3096$ |
| 15.1-e2 |
15.1-e |
$2$ |
$2$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{18} \cdot 5^{14} \) |
$4.42210$ |
$(-a), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$8.791298267$ |
1.95288393 |
\( \frac{2469187715650648441}{120135498046875} a^{2} - \frac{5586839672262719894}{120135498046875} a + \frac{2110702797111098206}{120135498046875} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 4\) , \( 0\) , \( -1259 a^{2} - 2232 a + 1366\) , \( 53456 a^{2} + 94738 a - 57960\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-1259a^{2}-2232a+1366\right){x}+53456a^{2}+94738a-57960$ |
| 15.1-f1 |
15.1-f |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{9} \cdot 5 \) |
$4.42210$ |
$(-a), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$28.87255204$ |
0.916242744 |
\( \frac{161948108}{1215} a^{2} + \frac{286415068}{1215} a - \frac{58287709}{405} \) |
\( \bigl[a + 1\) , \( 1\) , \( a^{2} - 4\) , \( 4 a^{2} - 14 a + 8\) , \( 2 a^{2} - 3 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+{x}^{2}+\left(4a^{2}-14a+8\right){x}+2a^{2}-3a-7$ |
| 15.2-a1 |
15.2-a |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{3} \cdot 5^{6} \) |
$4.42210$ |
$(-a+1), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$0.459108436$ |
$26.14516244$ |
2.28551062 |
\( \frac{313659392}{421875} a^{2} - \frac{31461376}{140625} a - \frac{597118976}{140625} \) |
\( \bigl[0\) , \( -a^{2} + 3\) , \( a\) , \( a^{2} + 2 a + 1\) , \( -a^{2} - a + 1\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(a^{2}+2a+1\right){x}-a^{2}-a+1$ |
| 15.2-b1 |
15.2-b |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3^{3} \cdot 5^{3} \) |
$4.42210$ |
$(-a+1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 3 \) |
$1$ |
$9.848690855$ |
0.937616272 |
\( \frac{28937478610943023}{3375} a^{2} - \frac{31381852004351744}{1125} a + \frac{12841572852578231}{1125} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} - 3\) , \( -1031 a^{2} + 3345 a - 1361\) , \( -47125 a^{2} + 153311 a - 62735\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-1031a^{2}+3345a-1361\right){x}-47125a^{2}+153311a-62735$ |
| 15.2-b2 |
15.2-b |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{6} \) |
$4.42210$ |
$(-a+1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$39.39476342$ |
0.937616272 |
\( \frac{9004442418733}{11390625} a^{2} - \frac{9751061147999}{3796875} a + \frac{4000156900226}{3796875} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} - 3\) , \( -66 a^{2} + 210 a - 76\) , \( -740 a^{2} + 2404 a - 981\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-66a^{2}+210a-76\right){x}-740a^{2}+2404a-981$ |
| 15.2-b3 |
15.2-b |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( 3^{12} \cdot 5^{12} \) |
$4.42210$ |
$(-a+1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$4.924345427$ |
0.937616272 |
\( -\frac{690215004655698497}{129746337890625} a^{2} + \frac{143098018930114816}{43248779296875} a + \frac{1377930394800900791}{43248779296875} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} - 3\) , \( -61 a^{2} + 195 a - 71\) , \( -851 a^{2} + 2765 a - 1131\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-61a^{2}+195a-71\right){x}-851a^{2}+2765a-1131$ |
| 15.2-b4 |
15.2-b |
$4$ |
$4$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{3} \cdot 5^{3} \) |
$4.42210$ |
$(-a+1), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$1$ |
$157.5790536$ |
0.937616272 |
\( \frac{2171102}{3375} a^{2} + \frac{3119}{1125} a + \frac{945019}{1125} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} - 3\) , \( -6 a^{2} + 15 a + 4\) , \( -11 a^{2} + 32 a - 10\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-6a^{2}+15a+4\right){x}-11a^{2}+32a-10$ |
| 21.1-a1 |
21.1-a |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3 \cdot 7 \) |
$4.67717$ |
$(-a+1), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.655422267$ |
$45.06379729$ |
2.81187239 |
\( \frac{105734}{21} a^{2} - \frac{19765}{7} a - \frac{216637}{7} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} + a - 5\) , \( a^{2} - 3\) , \( 8 a^{2} + 9 a - 18\) , \( 13 a^{2} + 21 a - 20\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(8a^{2}+9a-18\right){x}+13a^{2}+21a-20$ |
| 21.1-a2 |
21.1-a |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{3} \cdot 7^{3} \) |
$4.67717$ |
$(-a+1), (-a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$0.218474089$ |
$135.1913918$ |
2.81187239 |
\( -\frac{65048593}{9261} a^{2} + \frac{68573858}{3087} a - \frac{23247827}{3087} \) |
\( \bigl[a\) , \( a^{2} - 4\) , \( a^{2} + a - 3\) , \( -83 a^{2} + 43 a + 520\) , \( 373 a^{2} - 195 a - 2333\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-83a^{2}+43a+520\right){x}+373a^{2}-195a-2333$ |
| 21.2-a1 |
21.2-a |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
21.2 |
\( 3 \cdot 7 \) |
\( - 3^{7} \cdot 7^{2} \) |
$4.67717$ |
$(-a), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.265350312$ |
$10.39700124$ |
3.67707396 |
\( -\frac{3738811}{3969} a^{2} + \frac{12852733}{3969} a - \frac{6721532}{1323} \) |
\( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a^{2} + a - 4\) , \( 16 a^{2} - 4 a - 87\) , \( 69 a^{2} - 25 a - 406\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(16a^{2}-4a-87\right){x}+69a^{2}-25a-406$ |
| 24.1-a1 |
24.1-a |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{3} \cdot 3^{7} \) |
$4.78243$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.075752615$ |
$91.23296085$ |
4.60568331 |
\( \frac{992746090}{81} a^{2} - \frac{1032421211}{162} a - 76596409 \) |
\( \bigl[1\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( -59 a^{2} - 104 a + 66\) , \( -1091 a^{2} - 1935 a + 1179\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-59a^{2}-104a+66\right){x}-1091a^{2}-1935a+1179$ |
| 24.1-b1 |
24.1-b |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{6} \cdot 3^{3} \) |
$4.78243$ |
$(-a), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$40.78873207$ |
2.58878257 |
\( -\frac{13921}{36} a^{2} + \frac{10805}{18} a + \frac{6109}{4} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} + a - 5\) , \( a^{2} - 4\) , \( 6 a^{2} + 11 a - 4\) , \( 14 a^{2} + 22 a - 22\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(6a^{2}+11a-4\right){x}+14a^{2}+22a-22$ |
| 24.1-b2 |
24.1-b |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$4.78243$ |
$(-a), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$122.3661962$ |
2.58878257 |
\( \frac{339119}{192} a^{2} - \frac{112201}{96} a - \frac{84667}{8} \) |
\( \bigl[a\) , \( a^{2} - 4\) , \( 1\) , \( 235 a^{2} - 121 a - 1463\) , \( -4023 a^{2} + 2093 a + 25145\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(235a^{2}-121a-1463\right){x}-4023a^{2}+2093a+25145$ |
| 24.1-c1 |
24.1-c |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{36} \cdot 3^{2} \) |
$4.78243$ |
$(-a), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$1.485850320$ |
1.69747325 |
\( -\frac{50673535915}{12288} a^{2} - \frac{42573272605}{12288} a + \frac{16060645813}{6144} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 3\) , \( 1\) , \( -288 a^{2} - 471 a + 409\) , \( -6393 a^{2} - 11157 a + 7325\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-288a^{2}-471a+409\right){x}-6393a^{2}-11157a+7325$ |
| 24.1-c2 |
24.1-c |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{12} \cdot 3^{6} \) |
$4.78243$ |
$(-a), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$40.11795865$ |
1.69747325 |
\( \frac{12349213}{432} a^{2} - \frac{133792}{9} a - \frac{4823716}{27} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} - 4\) , \( 2756161 a^{2} - 1433120 a - 17224908\) , \( -4430277478 a^{2} + 2303608598 a + 27687467549\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(2756161a^{2}-1433120a-17224908\right){x}-4430277478a^{2}+2303608598a+27687467549$ |
| 24.2-a1 |
24.2-a |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( - 2^{18} \cdot 3^{2} \) |
$4.78243$ |
$(-a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$8.562046536$ |
4.34733335 |
\( \frac{6855698903}{576} a^{2} - \frac{296356339}{48} a - \frac{1789003231}{24} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 4\) , \( a^{2} - 4\) , \( 2127 a^{2} - 1108 a - 13295\) , \( 100244 a^{2} - 52125 a - 626489\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(2127a^{2}-1108a-13295\right){x}+100244a^{2}-52125a-626489$ |
| 24.2-a2 |
24.2-a |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( - 2^{6} \cdot 3^{6} \) |
$4.78243$ |
$(-a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$25.68613960$ |
4.34733335 |
\( -\frac{1487131948708237177}{2916} a^{2} + \frac{806376984862660399}{486} a - \frac{659944991378839451}{972} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - 4\) , \( 0\) , \( 41 a^{2} + 82 a - 47\) , \( -38 a^{2} - 81 a + 47\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(41a^{2}+82a-47\right){x}-38a^{2}-81a+47$ |
| 24.2-b1 |
24.2-b |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{15} \cdot 3^{8} \) |
$4.78243$ |
$(-a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$2.491035005$ |
$7.290542663$ |
3.45793092 |
\( -\frac{22933622129}{209952} a^{2} + \frac{3409582801}{69984} a + \frac{888520409}{69984} \) |
\( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 4\) , \( -3 a^{2} + 30 a - 17\) , \( -24 a^{2} + 110 a - 50\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+{x}^{2}+\left(-3a^{2}+30a-17\right){x}-24a^{2}+110a-50$ |
| 24.2-c1 |
24.2-c |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{9} \cdot 3^{6} \) |
$4.78243$ |
$(-a+1), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.138854636$ |
$112.7517745$ |
2.98098917 |
\( -\frac{35083049}{5832} a^{2} + \frac{5405305}{1944} a + \frac{73109177}{1944} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 4\) , \( a^{2} - 3\) , \( 189 a^{2} - 100 a - 1183\) , \( -2005 a^{2} + 1042 a + 12527\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(189a^{2}-100a-1183\right){x}-2005a^{2}+1042a+12527$ |
| 24.2-c2 |
24.2-c |
$2$ |
$3$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{3} \cdot 3^{2} \) |
$4.78243$ |
$(-a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.416563910$ |
$37.58392484$ |
2.98098917 |
\( -\frac{402173}{18} a^{2} + \frac{231769}{6} a + \frac{196213}{3} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( 1\) , \( a^{2} + a - 7\) , \( 4 a^{2} - 2 a - 27\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(a^{2}+a-7\right){x}+4a^{2}-2a-27$ |
| 24.2-d1 |
24.2-d |
$1$ |
$1$ |
3.3.993.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( - 2^{6} \cdot 3^{2} \) |
$4.78243$ |
$(-a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.032318780$ |
$119.0468213$ |
1.46514089 |
\( \frac{167}{36} a^{2} - \frac{673}{12} a + \frac{719}{6} \) |
\( \bigl[a\) , \( -a^{2} + a + 4\) , \( a^{2} + a - 4\) , \( -2 a^{2} - a + 8\) , \( 15 a^{2} + 27 a - 16\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-2a^{2}-a+8\right){x}+15a^{2}+27a-16$ |
*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.
