| 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 |
| 2.1-a1 |
2.1-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( -2 \) |
$2.01605$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.714638988$ |
0.888865463 |
\( -\frac{76166171122820337501}{2} a^{2} - 71070588105687328122 a - \frac{26573936673926179759}{2} \) |
\( \bigl[a^{2} - a - 3\) , \( -1\) , \( a^{2} - 2\) , \( -12952471 a^{2} + 34420720 a + 7749132\) , \( -75542410459 a^{2} + 200601387601 a + 45624539475\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}-{x}^{2}+\left(-12952471a^{2}+34420720a+7749132\right){x}-75542410459a^{2}+200601387601a+45624539475$ |
| 2.1-a2 |
2.1-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{5} \) |
$2.01605$ |
$(a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$89.32987356$ |
0.888865463 |
\( -1338 a^{2} - \frac{4995}{4} a + \frac{5371}{4} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 3\) , \( a + 1\) , \( -137 a^{2} + 360 a + 94\) , \( 4226 a^{2} - 11227 a - 2544\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-137a^{2}+360a+94\right){x}+4226a^{2}-11227a-2544$ |
| 2.1-a3 |
2.1-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$2.01605$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$25$ |
\( 3 \) |
$1$ |
$0.238212996$ |
0.888865463 |
\( \frac{2527677516010187499}{2} a^{2} - 1530200207852362500 a - 5996695099803199250 \) |
\( \bigl[1\) , \( a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( 490302 a^{2} - 593291 a - 2327384\) , \( 278561431 a^{2} - 337264349 a - 1321741427\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(490302a^{2}-593291a-2327384\right){x}+278561431a^{2}-337264349a-1321741427$ |
| 2.1-a4 |
2.1-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{15} \) |
$2.01605$ |
$(a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$29.77662452$ |
0.888865463 |
\( \frac{40467}{32} a^{2} - \frac{9609}{8} a - 5222 \) |
\( \bigl[1\) , \( a\) , \( a^{2} - a - 3\) , \( 4 a^{2} - 11\) , \( 6 a^{2} - 3 a - 22\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+a{x}^{2}+\left(4a^{2}-11\right){x}+6a^{2}-3a-22$ |
| 3.1-a1 |
3.1-a |
$4$ |
$6$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$2.15700$ |
$(a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.027193592$ |
$352.4453948$ |
0.715251864 |
\( -\frac{28942624}{9} a^{2} + \frac{11681984}{3} a + \frac{137333648}{9} \) |
\( \bigl[a^{2} - a - 2\) , \( -a - 1\) , \( 1\) , \( 60 a^{2} - 73 a - 285\) , \( -380 a^{2} + 460 a + 1803\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(60a^{2}-73a-285\right){x}-380a^{2}+460a+1803$ |
| 3.1-a2 |
3.1-a |
$4$ |
$6$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{6} \) |
$2.15700$ |
$(a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.081580776$ |
$117.4817982$ |
0.715251864 |
\( \frac{18274661792}{729} a^{2} + \frac{11368424960}{243} a + \frac{6377787920}{729} \) |
\( \bigl[a^{2} - a - 2\) , \( a\) , \( 1\) , \( 20 a^{2} - 29 a - 104\) , \( 45 a^{2} - 51 a - 208\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(20a^{2}-29a-104\right){x}+45a^{2}-51a-208$ |
| 3.1-a3 |
3.1-a |
$4$ |
$6$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$2.15700$ |
$(a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.163161553$ |
$117.4817982$ |
0.715251864 |
\( -\frac{10141696}{27} a^{2} + \frac{3792896}{9} a + \frac{50216960}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( a^{2} - a - 3\) , \( -24 a^{2} - 67 a - 45\) , \( 244 a^{2} + 400 a - 7\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-24a^{2}-67a-45\right){x}+244a^{2}+400a-7$ |
| 3.1-a4 |
3.1-a |
$4$ |
$6$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$2.15700$ |
$(a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.054387184$ |
$352.4453948$ |
0.715251864 |
\( \frac{8192}{3} a^{2} - 8192 a + \frac{8192}{3} \) |
\( \bigl[0\) , \( -a^{2} + 2 a + 4\) , \( a\) , \( a^{2} - a - 3\) , \( -1\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(a^{2}-a-3\right){x}-1$ |
| 3.1-b1 |
3.1-b |
$4$ |
$10$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$2.15700$ |
$(a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$0.791196430$ |
0.492043670 |
\( -\frac{23580594588909376}{9} a^{2} + \frac{9516797512518752}{3} a + \frac{111885814227156752}{9} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 4\) , \( 1\) , \( -1754900 a^{2} + 5387071 a - 1023733\) , \( -3049145021 a^{2} + 8514596427 a + 644486860\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-1754900a^{2}+5387071a-1023733\right){x}-3049145021a^{2}+8514596427a+644486860$ |
| 3.1-b2 |
3.1-b |
$4$ |
$10$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{10} \) |
$2.15700$ |
$(a^2-2a-2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$98.89955381$ |
0.492043670 |
\( -\frac{9349696}{59049} a^{2} + \frac{26473760}{19683} a + \frac{165172304}{59049} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 4\) , \( 1\) , \( 5 a^{2} - 5 a - 12\) , \( -7 a^{2} + 22 a + 7\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(5a^{2}-5a-12\right){x}-7a^{2}+22a+7$ |
| 3.1-b3 |
3.1-b |
$4$ |
$10$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{5} \) |
$2.15700$ |
$(a^2-2a-2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$197.7991076$ |
0.492043670 |
\( -\frac{1994752}{243} a^{2} + \frac{622592}{81} a + \frac{11141120}{243} \) |
\( \bigl[0\) , \( -a^{2} + 2\) , \( a\) , \( a^{2} + 2 a - 1\) , \( -a^{2} - a\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(a^{2}+2a-1\right){x}-a^{2}-a$ |
| 3.1-b4 |
3.1-b |
$4$ |
$10$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$2.15700$ |
$(a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$1.582392861$ |
0.492043670 |
\( \frac{42875328845753962496}{3} a^{2} - 37950988446668800000 a - \frac{25899620139672100864}{3} \) |
\( \bigl[0\) , \( -a^{2} + 2\) , \( a\) , \( -404559 a^{2} + 1091918 a + 193849\) , \( -263473120 a^{2} + 701229789 a + 154592433\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-404559a^{2}+1091918a+193849\right){x}-263473120a^{2}+701229789a+154592433$ |
| 9.2-a1 |
9.2-a |
$4$ |
$10$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{11} \) |
$2.59042$ |
$(a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$85.15931912$ |
2.118417240 |
\( -\frac{1994752}{243} a^{2} + \frac{622592}{81} a + \frac{11141120}{243} \) |
\( \bigl[0\) , \( 0\) , \( a^{2} - 2\) , \( a^{2} + 2 a\) , \( -3 a^{2} - 6 a - 2\bigr] \) |
${y}^2+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+2a\right){x}-3a^{2}-6a-2$ |
| 9.2-a2 |
9.2-a |
$4$ |
$10$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$2.59042$ |
$(a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$3.406372765$ |
2.118417240 |
\( \frac{42875328845753962496}{3} a^{2} - 37950988446668800000 a - \frac{25899620139672100864}{3} \) |
\( \bigl[0\) , \( 0\) , \( a^{2} - 2\) , \( -133859 a^{2} + 357962 a + 73674\) , \( -49059898 a^{2} + 130360486 a + 29392591\bigr] \) |
${y}^2+\left(a^{2}-2\right){y}={x}^{3}+\left(-133859a^{2}+357962a+73674\right){x}-49059898a^{2}+130360486a+29392591$ |
| 9.2-a3 |
9.2-a |
$4$ |
$10$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{16} \) |
$2.59042$ |
$(a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$42.57965956$ |
2.118417240 |
\( -\frac{9349696}{59049} a^{2} + \frac{26473760}{19683} a + \frac{165172304}{59049} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 2\) , \( -4 a - 1\) , \( -2 a^{2} + 3 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-4a-1\right){x}-2a^{2}+3a-2$ |
| 9.2-a4 |
9.2-a |
$4$ |
$10$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$2.59042$ |
$(a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$1.703186382$ |
2.118417240 |
\( -\frac{23580594588909376}{9} a^{2} + \frac{9516797512518752}{3} a + \frac{111885814227156752}{9} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 2\) , \( -663129 a^{2} + 1864280 a + 104258\) , \( -603355249 a^{2} + 1624683886 a + 299953028\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-663129a^{2}+1864280a+104258\right){x}-603355249a^{2}+1624683886a+299953028$ |
| 9.2-b1 |
9.2-b |
$4$ |
$6$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$2.59042$ |
$(a^2-2a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$194.9976089$ |
1.077943738 |
\( -\frac{28942624}{9} a^{2} + \frac{11681984}{3} a + \frac{137333648}{9} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 4\) , \( 1\) , \( 21 a^{2} - 49 a - 28\) , \( 726 a^{2} - 1945 a - 387\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(21a^{2}-49a-28\right){x}+726a^{2}-1945a-387$ |
| 9.2-b2 |
9.2-b |
$4$ |
$6$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$2.59042$ |
$(a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$21.66640099$ |
1.077943738 |
\( \frac{18274661792}{729} a^{2} + \frac{11368424960}{243} a + \frac{6377787920}{729} \) |
\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a^{2} - a - 3\) , \( 2 a^{2} + a - 9\) , \( -2 a^{2} + 11 a - 7\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a^{2}+a-9\right){x}-2a^{2}+11a-7$ |
| 9.2-b3 |
9.2-b |
$4$ |
$6$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$2.59042$ |
$(a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$21.66640099$ |
1.077943738 |
\( -\frac{10141696}{27} a^{2} + \frac{3792896}{9} a + \frac{50216960}{27} \) |
\( \bigl[0\) , \( a^{2} - 4\) , \( a^{2} - a - 3\) , \( -a^{2} + a + 3\) , \( -a^{2} - 3 a - 3\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-a^{2}+a+3\right){x}-a^{2}-3a-3$ |
| 9.2-b4 |
9.2-b |
$4$ |
$6$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$2.59042$ |
$(a^2-2a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$194.9976089$ |
1.077943738 |
\( \frac{8192}{3} a^{2} - 8192 a + \frac{8192}{3} \) |
\( \bigl[0\) , \( -a^{2} + 4\) , \( a\) , \( -7 a^{2} + 19 a + 9\) , \( 12 a^{2} - 34 a - 6\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-7a^{2}+19a+9\right){x}+12a^{2}-34a-6$ |
| 12.1-a1 |
12.1-a |
$8$ |
$12$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$2.71765$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$183.2759567$ |
1.139789956 |
\( -\frac{588544}{9} a^{2} + \frac{282656}{3} a + \frac{3039584}{9} \) |
\( \bigl[a^{2} - 3\) , \( a\) , \( a^{2} - 3\) , \( -a^{2} + 10 a - 3\) , \( 8 a^{2} - 12 a - 5\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+a{x}^{2}+\left(-a^{2}+10a-3\right){x}+8a^{2}-12a-5$ |
| 12.1-a2 |
12.1-a |
$8$ |
$12$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{3} \) |
$2.71765$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$122.1839711$ |
1.139789956 |
\( \frac{3243980224}{27} a^{2} + \frac{2017947520}{9} a + \frac{1131794368}{27} \) |
\( \bigl[a^{2} - 3\) , \( a\) , \( a + 1\) , \( -17 a^{2} + 47 a + 26\) , \( -18 a^{2} + 78 a - 46\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-17a^{2}+47a+26\right){x}-18a^{2}+78a-46$ |
| 12.1-a3 |
12.1-a |
$8$ |
$12$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$2.71765$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$366.5519135$ |
1.139789956 |
\( \frac{1293760}{3} a^{2} - 1144448 a - \frac{781376}{3} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 2\) , \( -1454 a^{2} + 3865 a + 876\) , \( 56098 a^{2} - 148970 a - 33861\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-1454a^{2}+3865a+876\right){x}+56098a^{2}-148970a-33861$ |
| 12.1-a4 |
12.1-a |
$8$ |
$12$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{6} \) |
$2.71765$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$61.09198559$ |
1.139789956 |
\( \frac{943823744}{729} a^{2} - \frac{833109472}{243} a - \frac{559677472}{729} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -a^{2} + 2 a + 6\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-a^{2}+2a+6\right){x}$ |
| 12.1-a5 |
12.1-a |
$8$ |
$12$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{12} \) |
$2.71765$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$15.27299639$ |
1.139789956 |
\( -\frac{16019567957620}{531441} a^{2} + \frac{6465449789504}{177147} a + \frac{76009811661524}{531441} \) |
\( \bigl[a^{2} - a - 2\) , \( -a - 1\) , \( a^{2} - 3\) , \( 15 a^{2} - 17 a - 83\) , \( 51 a^{2} - 54 a - 271\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(15a^{2}-17a-83\right){x}+51a^{2}-54a-271$ |
| 12.1-a6 |
12.1-a |
$8$ |
$12$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{3} \) |
$2.71765$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$30.54599279$ |
1.139789956 |
\( \frac{295486748097596}{27} a^{2} - \frac{261549344710720}{9} a - \frac{178494130128364}{27} \) |
\( \bigl[a^{2} - a - 2\) , \( -a - 1\) , \( a + 1\) , \( -38 a^{2} + 104 a + 8\) , \( -296 a^{2} + 778 a + 198\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-38a^{2}+104a+8\right){x}-296a^{2}+778a+198$ |
| 12.1-a7 |
12.1-a |
$8$ |
$12$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$2.71765$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$91.63797839$ |
1.139789956 |
\( -\frac{66635907124}{3} a^{2} + 26893262800 a + \frac{316175870180}{3} \) |
\( \bigl[a^{2} - a - 2\) , \( a\) , \( a^{2} - a - 2\) , \( -119 a^{2} + 346 a - 9\) , \( -1626 a^{2} + 4225 a + 1252\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+a{x}^{2}+\left(-119a^{2}+346a-9\right){x}-1626a^{2}+4225a+1252$ |
| 12.1-a8 |
12.1-a |
$8$ |
$12$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{4} \) |
$2.71765$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$45.81898919$ |
1.139789956 |
\( \frac{28379502140}{81} a^{2} + \frac{17653936784}{27} a + \frac{9901591172}{81} \) |
\( \bigl[a^{2} - a - 2\) , \( a\) , \( 0\) , \( 64 a^{2} - 164 a - 45\) , \( 335 a^{2} - 887 a - 203\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+a{x}^{2}+\left(64a^{2}-164a-45\right){x}+335a^{2}-887a-203$ |
| 14.1-a1 |
14.1-a |
$2$ |
$3$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{6} \) |
$2.78837$ |
$(a+1), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.044351262$ |
$76.21402778$ |
1.009023926 |
\( -\frac{11703738889}{235298} a^{2} - \frac{10944764857}{117649} a - \frac{4094759737}{235298} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( -4314 a^{2} - 8050 a - 1502\) , \( 395647 a^{2} + 738355 a + 138038\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-4314a^{2}-8050a-1502\right){x}+395647a^{2}+738355a+138038$ |
| 14.1-a2 |
14.1-a |
$2$ |
$3$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7^{2} \) |
$2.78837$ |
$(a+1), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.014783754$ |
$228.6420833$ |
1.009023926 |
\( -\frac{3707262}{49} a^{2} + \frac{9847594}{49} a + \frac{4480743}{98} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 3\) , \( a\) , \( 4 a^{2} + 7 a + 4\) , \( 34 a^{2} + 65 a + 13\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(4a^{2}+7a+4\right){x}+34a^{2}+65a+13$ |
| 16.1-a1 |
16.1-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{27} \) |
$2.85112$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.070396145$ |
$41.43661188$ |
1.741500805 |
\( \frac{40467}{32} a^{2} - \frac{9609}{8} a - 5222 \) |
\( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 3\) , \( 26 a^{2} + 46 a + 6\) , \( 33 a^{2} + 60 a + 9\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(26a^{2}+46a+6\right){x}+33a^{2}+60a+9$ |
| 16.1-a2 |
16.1-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{15} \) |
$2.85112$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.351980726$ |
$8.287322377$ |
1.741500805 |
\( \frac{2527677516010187499}{2} a^{2} - 1530200207852362500 a - 5996695099803199250 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 2\) , \( -10471 a^{2} + 36781 a - 19407\) , \( -2510622 a^{2} + 6102902 a + 3132862\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-10471a^{2}+36781a-19407\right){x}-2510622a^{2}+6102902a+3132862$ |
| 16.1-a3 |
16.1-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{17} \) |
$2.85112$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.023465381$ |
$124.3098356$ |
1.741500805 |
\( -1338 a^{2} - \frac{4995}{4} a + \frac{5371}{4} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - a - 2\) , \( -9399 a^{2} + 24957 a + 5679\) , \( 2504627 a^{2} - 6650893 a - 1512966\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-9399a^{2}+24957a+5679\right){x}+2504627a^{2}-6650893a-1512966$ |
| 16.1-a4 |
16.1-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{13} \) |
$2.85112$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$0.117326908$ |
$24.86196713$ |
1.741500805 |
\( -\frac{76166171122820337501}{2} a^{2} - 71070588105687328122 a - \frac{26573936673926179759}{2} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 3\) , \( a + 1\) , \( -906999323 a^{2} + 2408484771 a + 547888445\) , \( -44175555341827 a^{2} + 117305641879426 a + 26685045551577\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-906999323a^{2}+2408484771a+547888445\right){x}-44175555341827a^{2}+117305641879426a+26685045551577$ |
| 18.1-a1 |
18.1-a |
$2$ |
$2$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{4} \) |
$2.90764$ |
$(a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.373073252$ |
$33.96356274$ |
0.945601018 |
\( \frac{838861025}{18} a^{2} + \frac{170721145}{9} a + \frac{34746833}{18} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 2\) , \( 0\) , \( 4 a - 12\) , \( -16 a^{2} + 37 a + 25\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(4a-12\right){x}-16a^{2}+37a+25$ |
| 18.1-a2 |
18.1-a |
$2$ |
$2$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{2} \) |
$2.90764$ |
$(a+1), (a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.186536626$ |
$67.92712548$ |
0.945601018 |
\( -100 a^{2} + \frac{41725}{6} a + \frac{15593}{6} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 2\) , \( 0\) , \( -a + 3\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-a+3\right){x}$ |
| 18.2-a1 |
18.2-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{6} \) |
$2.90764$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$6.267128581$ |
0.866114724 |
\( -\frac{76166171122820337501}{2} a^{2} - 71070588105687328122 a - \frac{26573936673926179759}{2} \) |
\( \bigl[a^{2} - a - 3\) , \( a - 1\) , \( a\) , \( -80662877486 a^{2} + 214195625506 a + 48725868589\) , \( -37049737283258134 a^{2} + 98383442607311942 a + 22380565881296748\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-80662877486a^{2}+214195625506a+48725868589\right){x}-37049737283258134a^{2}+98383442607311942a+22380565881296748$ |
| 18.2-a2 |
18.2-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{5} \cdot 3^{6} \) |
$2.90764$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$156.6782145$ |
0.866114724 |
\( -1338 a^{2} - \frac{4995}{4} a + \frac{5371}{4} \) |
\( \bigl[a^{2} - a - 3\) , \( 0\) , \( 1\) , \( -835918 a^{2} + 2219731 a + 504954\) , \( 2090099535 a^{2} - 5550138887 a - 1262562538\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+{y}={x}^{3}+\left(-835918a^{2}+2219731a+504954\right){x}+2090099535a^{2}-5550138887a-1262562538$ |
| 18.2-a3 |
18.2-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{6} \) |
$2.90764$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$17.40869050$ |
0.866114724 |
\( \frac{40467}{32} a^{2} - \frac{9609}{8} a - 5222 \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( 2 a^{2} - 2 a + 1\) , \( -3 a^{2} + 10 a\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(2a^{2}-2a+1\right){x}-3a^{2}+10a$ |
| 18.2-a4 |
18.2-a |
$4$ |
$15$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{6} \) |
$2.90764$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$0.696347620$ |
0.866114724 |
\( \frac{2527677516010187499}{2} a^{2} - 1530200207852362500 a - 5996695099803199250 \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -1446116 a^{2} + 3894533 a + 717474\) , \( -1771198249 a^{2} + 4711963504 a + 1045135808\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-1446116a^{2}+3894533a+717474\right){x}-1771198249a^{2}+4711963504a+1045135808$ |
| 21.1-a1 |
21.1-a |
$2$ |
$2$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3 \cdot 7^{6} \) |
$2.98332$ |
$(a^2-2a-2), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$69.77912411$ |
1.735820589 |
\( \frac{2363138302249}{352947} a^{2} - \frac{2064938352443}{117649} a - \frac{1408185158861}{352947} \) |
\( \bigl[a^{2} - a - 3\) , \( a\) , \( 0\) , \( -4 a - 8\) , \( -3 a^{2} - 15 a - 15\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+a{x}^{2}+\left(-4a-8\right){x}-3a^{2}-15a-15$ |
| 21.1-a2 |
21.1-a |
$2$ |
$2$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{3} \) |
$2.98332$ |
$(a^2-2a-2), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$69.77912411$ |
1.735820589 |
\( -\frac{3059155}{3087} a^{2} + \frac{2502782}{1029} a + \frac{2679176}{3087} \) |
\( \bigl[a^{2} - a - 3\) , \( a\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+a{x}^{2}+\left(a+2\right){x}$ |
| 22.1-a1 |
22.1-a |
$2$ |
$3$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{7} \cdot 11^{3} \) |
$3.00654$ |
$(a+1), (a^2-2a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$10.37732228$ |
1.548873241 |
\( -\frac{105531324000853}{10648} a^{2} + \frac{35029008270285}{1331} a + \frac{63748050694197}{10648} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 3\) , \( -7 a^{2} + 13 a + 9\) , \( -9 a^{2} + 22 a + 6\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-7a^{2}+13a+9\right){x}-9a^{2}+22a+6$ |
| 22.1-a2 |
22.1-a |
$2$ |
$3$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{21} \cdot 11 \) |
$3.00654$ |
$(a+1), (a^2-2a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$31.13196685$ |
1.548873241 |
\( -\frac{609343}{1408} a^{2} + \frac{262173}{176} a + \frac{234351}{704} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 2 a - 4\) , \( 0\) , \( -299275 a^{2} + 794714 a + 180786\) , \( -198828860 a^{2} + 527978588 a + 120106181\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-299275a^{2}+794714a+180786\right){x}-198828860a^{2}+527978588a+120106181$ |
| 22.1-b1 |
22.1-b |
$2$ |
$3$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{3} \cdot 11 \) |
$3.00654$ |
$(a+1), (a^2-2a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$18.15053650$ |
2.709068826 |
\( \frac{349366983357}{22} a^{2} - \frac{211499066078}{11} a - \frac{828842783673}{11} \) |
\( \bigl[a\) , \( a\) , \( a^{2} - a - 3\) , \( 3 a^{2} - 6 a - 3\) , \( -5 a^{2} + 15 a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+a{x}^{2}+\left(3a^{2}-6a-3\right){x}-5a^{2}+15a+1$ |
| 22.1-b2 |
22.1-b |
$2$ |
$3$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2 \cdot 11^{3} \) |
$3.00654$ |
$(a+1), (a^2-2a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$54.45160952$ |
2.709068826 |
\( \frac{1837139}{2662} a^{2} - \frac{933232}{1331} a - \frac{9619627}{2662} \) |
\( \bigl[1\) , \( a\) , \( a^{2} - 2\) , \( -1254756 a^{2} + 3331932 a + 757959\) , \( 2792296240 a^{2} - 7414781780 a - 1686737197\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+a{x}^{2}+\left(-1254756a^{2}+3331932a+757959\right){x}+2792296240a^{2}-7414781780a-1686737197$ |
| 24.1-a1 |
24.1-a |
$6$ |
$8$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$3.05045$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$140.2422947$ |
1.744328735 |
\( \frac{184384}{9} a^{2} - \frac{164480}{3} a - \frac{99776}{9} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - a - 2\) , \( -40364982 a^{2} + 107130024 a + 24546176\) , \( 250358677116 a^{2} - 664817719080 a - 151220294362\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-40364982a^{2}+107130024a+24546176\right){x}+250358677116a^{2}-664817719080a-151220294362$ |
| 24.1-a2 |
24.1-a |
$6$ |
$8$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$3.05045$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$140.2422947$ |
1.744328735 |
\( \frac{65600}{81} a^{2} + \frac{46880}{27} a + \frac{200864}{81} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( 0\) , \( -141366 a^{2} + 377810 a + 78463\) , \( -12220990 a^{2} + 32420481 a + 7473040\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-141366a^{2}+377810a+78463\right){x}-12220990a^{2}+32420481a+7473040$ |
| 24.1-a3 |
24.1-a |
$6$ |
$8$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$3.05045$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$35.06057367$ |
1.744328735 |
\( \frac{116047844}{9} a^{2} + \frac{71000072}{3} a + \frac{40336292}{9} \) |
\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a + 1\) , \( -3610 a^{2} + 9775 a + 1653\) , \( -222137 a^{2} + 591331 a + 130019\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-3610a^{2}+9775a+1653\right){x}-222137a^{2}+591331a+130019$ |
| 24.1-a4 |
24.1-a |
$6$ |
$8$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$3.05045$ |
$(a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$4.382571709$ |
1.744328735 |
\( \frac{184389350588}{3} a^{2} - 164623353602 a - \frac{99246095086}{3} \) |
\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a + 1\) , \( -57745 a^{2} + 156305 a + 26393\) , \( -14288734 a^{2} + 38048085 a + 8329931\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-57745a^{2}+156305a+26393\right){x}-14288734a^{2}+38048085a+8329931$ |
*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.
