| 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 |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$3.80475$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$59.88002378$ |
2.533410605 |
\( \frac{18546184}{729} a^{2} - \frac{15879673}{729} a - \frac{93317327}{729} \) |
\( \bigl[a^{2} + a - 6\) , \( -a + 1\) , \( 0\) , \( 134523 a^{2} + 231702 a - 445064\) , \( -25849654 a^{2} - 44566239 a + 85400355\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(134523a^{2}+231702a-445064\right){x}-25849654a^{2}-44566239a+85400355$ |
| 3.1-a2 |
3.1-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$3.80475$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$29.94001189$ |
2.533410605 |
\( -\frac{1211556145071239}{531441} a^{2} - \frac{181422525708217}{531441} a + \frac{9483860813000392}{531441} \) |
\( \bigl[a^{2} + a - 6\) , \( -a + 1\) , \( 0\) , \( -595362 a^{2} - 1029733 a + 1957451\) , \( -218641073 a^{2} - 377080991 a + 721953419\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-595362a^{2}-1029733a+1957451\right){x}-218641073a^{2}-377080991a+721953419$ |
| 3.1-a3 |
3.1-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$3.80475$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$89.82003567$ |
2.533410605 |
\( \frac{1830486664}{81} a^{2} - \frac{6074269615}{81} a + \frac{4564377361}{81} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + a + 6\) , \( a + 1\) , \( 11 a^{2} + 5 a - 84\) , \( 65 a^{2} + 13 a - 503\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(11a^{2}+5a-84\right){x}+65a^{2}+13a-503$ |
| 3.1-a4 |
3.1-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$3.80475$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$179.6400713$ |
2.533410605 |
\( \frac{3817}{9} a^{2} - \frac{41086}{9} a + \frac{49897}{9} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + a + 6\) , \( a + 1\) , \( -4 a^{2} + 41\) , \( -3 a^{2} + 3 a + 29\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-4a^{2}+41\right){x}-3a^{2}+3a+29$ |
| 3.1-b1 |
3.1-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$3.80475$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$41.69244451$ |
1.175952339 |
\( \frac{1830486664}{81} a^{2} - \frac{6074269615}{81} a + \frac{4564377361}{81} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} + a - 6\) , \( a\) , \( -10 a^{2} + 43 a - 36\) , \( -74 a^{2} + 289 a - 234\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-10a^{2}+43a-36\right){x}-74a^{2}+289a-234$ |
| 3.1-b2 |
3.1-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$3.80475$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$83.38488902$ |
1.175952339 |
\( \frac{3817}{9} a^{2} - \frac{41086}{9} a + \frac{49897}{9} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} + a - 6\) , \( a\) , \( 3 a - 1\) , \( -a^{2} + 7 a - 7\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(3a-1\right){x}-a^{2}+7a-7$ |
| 3.1-b3 |
3.1-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$3.80475$ |
$(-a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$250.1546670$ |
1.175952339 |
\( \frac{18546184}{729} a^{2} - \frac{15879673}{729} a - \frac{93317327}{729} \) |
\( \bigl[a + 1\) , \( -a\) , \( a^{2} - 5\) , \( 399413 a^{2} + 688565 a - 1319676\) , \( 133141305 a^{2} + 229529824 a - 439901186\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}-a{x}^{2}+\left(399413a^{2}+688565a-1319676\right){x}+133141305a^{2}+229529824a-439901186$ |
| 3.1-b4 |
3.1-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$3.80475$ |
$(-a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$125.0773335$ |
1.175952339 |
\( -\frac{1211556145071239}{531441} a^{2} - \frac{181422525708217}{531441} a + \frac{9483860813000392}{531441} \) |
\( \bigl[a + 1\) , \( -a\) , \( a^{2} - 5\) , \( -1775717 a^{2} - 3061335 a + 5866789\) , \( 1117676178 a^{2} + 1926825603 a - 3692820244\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}-a{x}^{2}+\left(-1775717a^{2}-3061335a+5866789\right){x}+1117676178a^{2}+1926825603a-3692820244$ |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{14} \) |
$4.56927$ |
$(-a+3), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.065062043$ |
1.714345598 |
\( -\frac{572710869954935236}{729} a^{2} - \frac{85759680077309951}{729} a + \frac{4483085332584849155}{729} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 6\) , \( a^{2} + a - 5\) , \( 40 a^{2} - 127 a - 694\) , \( 836 a^{2} - 1379 a - 10867\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(40a^{2}-127a-694\right){x}+836a^{2}-1379a-10867$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{16} \) |
$4.56927$ |
$(-a+3), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$10.13012408$ |
1.714345598 |
\( \frac{5922846370225}{531441} a^{2} + \frac{869955487334}{531441} a - \frac{46317078190511}{531441} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 6\) , \( a^{2} + a - 5\) , \( -7 a - 19\) , \( 17 a^{2} - 37 a - 247\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-7a-19\right){x}+17a^{2}-37a-247$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{16} \) |
$4.56927$ |
$(-a+3), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$30.39037225$ |
1.714345598 |
\( \frac{638020}{729} a^{2} - \frac{2307097}{729} a + \frac{7351}{3} \) |
\( \bigl[a\) , \( a^{2} + a - 5\) , \( a^{2} - 5\) , \( 465 a^{2} + 781 a - 1589\) , \( 24180 a^{2} + 41186 a - 81328\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(465a^{2}+781a-1589\right){x}+24180a^{2}+41186a-81328$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{26} \) |
$4.56927$ |
$(-a+3), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$15.19518612$ |
1.714345598 |
\( -\frac{13990362643}{531441} a^{2} - \frac{1474816643}{531441} a + \frac{12368265940}{59049} \) |
\( \bigl[a\) , \( a^{2} + a - 5\) , \( a^{2} - 5\) , \( -3715 a^{2} - 7144 a + 10156\) , \( 265264 a^{2} + 442420 a - 919210\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-3715a^{2}-7144a+10156\right){x}+265264a^{2}+442420a-919210$ |
| 9.1-b1 |
9.1-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{16} \) |
$4.56927$ |
$(-a+3), (a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.244868234$ |
$126.7871907$ |
3.502677731 |
\( \frac{5922846370225}{531441} a^{2} + \frac{869955487334}{531441} a - \frac{46317078190511}{531441} \) |
\( \bigl[a^{2} - 6\) , \( a + 1\) , \( a^{2} + a - 6\) , \( -13 a^{2} - 19 a + 49\) , \( 89 a^{2} + 155 a - 285\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-13a^{2}-19a+49\right){x}+89a^{2}+155a-285$ |
| 9.1-b2 |
9.1-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{14} \) |
$4.56927$ |
$(-a+3), (a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.489736468$ |
$63.39359538$ |
3.502677731 |
\( -\frac{572710869954935236}{729} a^{2} - \frac{85759680077309951}{729} a + \frac{4483085332584849155}{729} \) |
\( \bigl[a^{2} - 6\) , \( a + 1\) , \( a^{2} + a - 6\) , \( -248 a^{2} - 429 a + 814\) , \( 4145 a^{2} + 7143 a - 13695\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-248a^{2}-429a+814\right){x}+4145a^{2}+7143a-13695$ |
| 9.1-b3 |
9.1-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{16} \) |
$4.56927$ |
$(-a+3), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.081622744$ |
$42.26239692$ |
3.502677731 |
\( \frac{638020}{729} a^{2} - \frac{2307097}{729} a + \frac{7351}{3} \) |
\( \bigl[1\) , \( -a^{2} - a + 6\) , \( a + 1\) , \( 1341 a^{2} + 2312 a - 4429\) , \( -118606 a^{2} - 204470 a + 391880\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(1341a^{2}+2312a-4429\right){x}-118606a^{2}-204470a+391880$ |
| 9.1-b4 |
9.1-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{26} \) |
$4.56927$ |
$(-a+3), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.163245489$ |
$21.13119846$ |
3.502677731 |
\( -\frac{13990362643}{531441} a^{2} - \frac{1474816643}{531441} a + \frac{12368265940}{59049} \) |
\( \bigl[1\) , \( -a^{2} - a + 6\) , \( a + 1\) , \( -12429 a^{2} - 21443 a + 41021\) , \( -1344573 a^{2} - 2317954 a + 4442582\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-12429a^{2}-21443a+41021\right){x}-1344573a^{2}-2317954a+4442582$ |
| 9.2-a1 |
9.2-a |
$1$ |
$1$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{9} \) |
$4.56927$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 2 \) |
$0.152226522$ |
$88.19087589$ |
2.271943846 |
\( -287 a^{2} - 46 a + 2251 \) |
\( \bigl[a^{2} + a - 6\) , \( -a^{2} + a + 5\) , \( 1\) , \( a^{2} - 2 a + 3\) , \( 6 a^{2} - 3 a - 33\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(a^{2}-2a+3\right){x}+6a^{2}-3a-33$ |
| 9.2-b1 |
9.2-b |
$1$ |
$1$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{7} \) |
$4.56927$ |
$(a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$50.62597628$ |
2.855852467 |
\( -\frac{171170}{3} a^{2} + \frac{659137}{3} a - 174840 \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + 6\) , \( a + 1\) , \( -7 a^{2} + a + 47\) , \( -7 a^{2} + 2 a + 43\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-7a^{2}+a+47\right){x}-7a^{2}+2a+43$ |
| 9.2-c1 |
9.2-c |
$1$ |
$1$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{7} \) |
$4.56927$ |
$(a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$31.38259050$ |
3.540634872 |
\( -\frac{171170}{3} a^{2} + \frac{659137}{3} a - 174840 \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 5\) , \( 0\) , \( 2 a^{2} + a - 13\) , \( 8 a^{2} + a - 64\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(2a^{2}+a-13\right){x}+8a^{2}+a-64$ |
| 9.2-d1 |
9.2-d |
$1$ |
$1$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{9} \) |
$4.56927$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 2 \) |
$0.077810295$ |
$151.3339940$ |
1.992769974 |
\( -287 a^{2} - 46 a + 2251 \) |
\( \bigl[a + 1\) , \( a^{2} - a - 5\) , \( a + 1\) , \( 3 a^{2} - 15 a + 15\) , \( 118 a^{2} - 457 a + 367\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(3a^{2}-15a+15\right){x}+118a^{2}-457a+367$ |
| 9.3-a1 |
9.3-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{12} \) |
$4.56927$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$76.40404711$ |
2.155007196 |
\( \frac{18546184}{729} a^{2} - \frac{15879673}{729} a - \frac{93317327}{729} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 7\) , \( 1\) , \( 210 a^{2} + 360 a - 686\) , \( 1550 a^{2} + 2669 a - 5119\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(210a^{2}+360a-686\right){x}+1550a^{2}+2669a-5119$ |
| 9.3-a2 |
9.3-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{18} \) |
$4.56927$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$76.40404711$ |
2.155007196 |
\( -\frac{1211556145071239}{531441} a^{2} - \frac{181422525708217}{531441} a + \frac{9483860813000392}{531441} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 7\) , \( 1\) , \( -935 a^{2} - 1615 a + 3094\) , \( 13777 a^{2} + 23750 a - 45511\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-935a^{2}-1615a+3094\right){x}+13777a^{2}+23750a-45511$ |
| 9.3-a3 |
9.3-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.56927$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$76.40404711$ |
2.155007196 |
\( \frac{3817}{9} a^{2} - \frac{41086}{9} a + \frac{49897}{9} \) |
\( \bigl[a\) , \( -a\) , \( a^{2} + a - 6\) , \( -a^{2} - 2 a + 6\) , \( -a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}-a{x}^{2}+\left(-a^{2}-2a+6\right){x}-a-2$ |
| 9.3-a4 |
9.3-a |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{10} \) |
$4.56927$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$76.40404711$ |
2.155007196 |
\( \frac{1830486664}{81} a^{2} - \frac{6074269615}{81} a + \frac{4564377361}{81} \) |
\( \bigl[a\) , \( -a\) , \( a^{2} + a - 6\) , \( -6 a^{2} + 3 a + 6\) , \( -a^{2} - 23 a + 25\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}-a{x}^{2}+\left(-6a^{2}+3a+6\right){x}-a^{2}-23a+25$ |
| 9.3-b1 |
9.3-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{10} \) |
$4.56927$ |
$(-a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$164.6009083$ |
0.515848389 |
\( \frac{1830486664}{81} a^{2} - \frac{6074269615}{81} a + \frac{4564377361}{81} \) |
\( \bigl[a^{2} - 6\) , \( 0\) , \( a^{2} - 6\) , \( 4 a^{2} - 39\) , \( 18 a^{2} + 4 a - 137\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(4a^{2}-39\right){x}+18a^{2}+4a-137$ |
| 9.3-b2 |
9.3-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.56927$ |
$(-a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$164.6009083$ |
0.515848389 |
\( \frac{3817}{9} a^{2} - \frac{41086}{9} a + \frac{49897}{9} \) |
\( \bigl[a^{2} - 6\) , \( 0\) , \( a^{2} - 6\) , \( -a^{2} + 6\) , \( -a^{2} + 7\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+6\right){x}-a^{2}+7$ |
| 9.3-b3 |
9.3-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{12} \) |
$4.56927$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$18.28898981$ |
0.515848389 |
\( \frac{18546184}{729} a^{2} - \frac{15879673}{729} a - \frac{93317327}{729} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + a + 5\) , \( 0\) , \( 73 a^{2} + 123 a - 237\) , \( -144 a^{2} - 255 a + 448\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(73a^{2}+123a-237\right){x}-144a^{2}-255a+448$ |
| 9.3-b4 |
9.3-b |
$4$ |
$6$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{18} \) |
$4.56927$ |
$(-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$18.28898981$ |
0.515848389 |
\( -\frac{1211556145071239}{531441} a^{2} - \frac{181422525708217}{531441} a + \frac{9483860813000392}{531441} \) |
\( \bigl[a^{2} + a - 5\) , \( -a^{2} + a + 5\) , \( 0\) , \( -282 a^{2} - 537 a + 798\) , \( -3115 a^{2} - 5758 a + 9169\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-282a^{2}-537a+798\right){x}-3115a^{2}-5758a+9169$ |
| 13.3-a1 |
13.3-a |
$3$ |
$9$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
13.3 |
\( 13 \) |
\( 13 \) |
$4.85807$ |
$(-a^2-a+4)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$292.1195091$ |
0.915483273 |
\( \frac{6341531676672}{13} a^{2} + \frac{949606547456}{13} a - \frac{49640464818176}{13} \) |
\( \bigl[0\) , \( a^{2} + a - 5\) , \( a + 1\) , \( -5\) , \( -3 a^{2} - 3 a + 19\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}-5{x}-3a^{2}-3a+19$ |
| 13.3-a2 |
13.3-a |
$3$ |
$9$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
13.3 |
\( 13 \) |
\( 13^{3} \) |
$4.85807$ |
$(-a^2-a+4)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$97.37316972$ |
0.915483273 |
\( \frac{2465067008}{2197} a^{2} + \frac{4242079744}{2197} a - \frac{8166293504}{2197} \) |
\( \bigl[0\) , \( 1\) , \( a^{2} + a - 6\) , \( -773 a^{2} - 1339 a + 2536\) , \( -25013 a^{2} - 43111 a + 82673\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){y}={x}^{3}+{x}^{2}+\left(-773a^{2}-1339a+2536\right){x}-25013a^{2}-43111a+82673$ |
| 13.3-a3 |
13.3-a |
$3$ |
$9$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
13.3 |
\( 13 \) |
\( 13 \) |
$4.85807$ |
$(-a^2-a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$3.606413693$ |
0.915483273 |
\( \frac{1417224386714174820352}{13} a^{2} + \frac{2443233178540991471616}{13} a - \frac{4682534221686619037696}{13} \) |
\( \bigl[0\) , \( 1\) , \( a^{2} + a - 6\) , \( -62963 a^{2} - 108509 a + 208136\) , \( -18062441 a^{2} - 31138840 a + 59678686\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){y}={x}^{3}+{x}^{2}+\left(-62963a^{2}-108509a+208136\right){x}-18062441a^{2}-31138840a+59678686$ |
| 13.3-b1 |
13.3-b |
$3$ |
$9$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
13.3 |
\( 13 \) |
\( 13^{3} \) |
$4.85807$ |
$(-a^2-a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs |
$1$ |
\( 1 \) |
$0.637310789$ |
$81.79156178$ |
4.410759600 |
\( \frac{2465067008}{2197} a^{2} + \frac{4242079744}{2197} a - \frac{8166293504}{2197} \) |
\( \bigl[0\) , \( -a + 1\) , \( a^{2} - 5\) , \( -2309 a^{2} - 3982 a + 7630\) , \( 128122 a^{2} + 220876 a - 423320\bigr] \) |
${y}^2+\left(a^{2}-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2309a^{2}-3982a+7630\right){x}+128122a^{2}+220876a-423320$ |
| 13.3-b2 |
13.3-b |
$3$ |
$9$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
13.3 |
\( 13 \) |
\( 13 \) |
$4.85807$ |
$(-a^2-a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1.911932369$ |
$27.26385392$ |
4.410759600 |
\( \frac{1417224386714174820352}{13} a^{2} + \frac{2443233178540991471616}{13} a - \frac{4682534221686619037696}{13} \) |
\( \bigl[0\) , \( -a + 1\) , \( a^{2} - 5\) , \( -187059 a^{2} - 322482 a + 618050\) , \( 92545433 a^{2} + 159544299 a - 305771736\bigr] \) |
${y}^2+\left(a^{2}-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-187059a^{2}-322482a+618050\right){x}+92545433a^{2}+159544299a-305771736$ |
| 13.3-b3 |
13.3-b |
$3$ |
$9$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
13.3 |
\( 13 \) |
\( 13 \) |
$4.85807$ |
$(-a^2-a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1.911932369$ |
$27.26385392$ |
4.410759600 |
\( \frac{6341531676672}{13} a^{2} + \frac{949606547456}{13} a - \frac{49640464818176}{13} \) |
\( \bigl[0\) , \( -a^{2} + a + 7\) , \( a^{2} - 6\) , \( -10 a^{2} + 4 a + 24\) , \( 5 a^{2} - 78 a + 89\bigr] \) |
${y}^2+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-10a^{2}+4a+24\right){x}+5a^{2}-78a+89$ |
| 15.1-a1 |
15.1-a |
$1$ |
$1$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5^{8} \) |
$4.97532$ |
$(a-2), (a^2+a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$15.58340879$ |
3.516291021 |
\( -\frac{98647706495558}{1171875} a^{2} - \frac{170062438373699}{1171875} a + \frac{108647077995156}{390625} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 5\) , \( a^{2} - 5\) , \( -47 a^{2} - 79 a + 156\) , \( -342 a^{2} - 589 a + 1129\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-47a^{2}-79a+156\right){x}-342a^{2}-589a+1129$ |
| 15.1-b1 |
15.1-b |
$1$ |
$1$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{11} \cdot 5^{4} \) |
$4.97532$ |
$(a-2), (a^2+a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 11 \) |
$0.024570724$ |
$34.66856998$ |
3.171466840 |
\( -\frac{129241459}{455625} a^{2} - \frac{139735327}{455625} a + \frac{142620071}{50625} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} - a - 5\) , \( a^{2} + a - 5\) , \( 6 a^{2} - 20 a + 10\) , \( 19 a^{2} - 75 a + 66\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(6a^{2}-20a+10\right){x}+19a^{2}-75a+66$ |
| 15.1-c1 |
15.1-c |
$1$ |
$1$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{11} \cdot 5^{4} \) |
$4.97532$ |
$(a-2), (a^2+a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.174072143$ |
$62.72520625$ |
1.847800107 |
\( -\frac{129241459}{455625} a^{2} - \frac{139735327}{455625} a + \frac{142620071}{50625} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 7\) , \( a^{2} - 5\) , \( 35 a^{2} + 4 a - 264\) , \( 191 a^{2} + 31 a - 1496\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(35a^{2}+4a-264\right){x}+191a^{2}+31a-1496$ |
| 15.1-d1 |
15.1-d |
$1$ |
$1$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5^{8} \) |
$4.97532$ |
$(a-2), (a^2+a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$71.34998802$ |
4.024910813 |
\( -\frac{98647706495558}{1171875} a^{2} - \frac{170062438373699}{1171875} a + \frac{108647077995156}{390625} \) |
\( \bigl[a^{2} - 6\) , \( a^{2} + a - 6\) , \( a^{2} - 5\) , \( -135 a^{2} - 234 a + 440\) , \( 1615 a^{2} + 2784 a - 5339\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-135a^{2}-234a+440\right){x}+1615a^{2}+2784a-5339$ |
| 15.2-a1 |
15.2-a |
$2$ |
$3$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{21} \cdot 5^{2} \) |
$4.97532$ |
$(-a+3), (a^2+a-5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$1$ |
$16.76681548$ |
2.206935939 |
\( \frac{16617904504832}{261508830075} a^{2} - \frac{17777360175104}{261508830075} a + \frac{188962230960128}{261508830075} \) |
\( \bigl[0\) , \( a^{2} + a - 5\) , \( a^{2} - 6\) , \( -26 a^{2} - 3 a + 210\) , \( 182 a^{2} + 28 a - 1422\bigr] \) |
${y}^2+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-26a^{2}-3a+210\right){x}+182a^{2}+28a-1422$ |
| 15.2-a2 |
15.2-a |
$2$ |
$3$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{7} \cdot 5^{6} \) |
$4.97532$ |
$(-a+3), (a^2+a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$5.588938494$ |
2.206935939 |
\( \frac{825621512192}{34171875} a^{2} + \frac{136621490176}{34171875} a - \frac{6558260396032}{34171875} \) |
\( \bigl[0\) , \( 1\) , \( a^{2} - 5\) , \( 2886 a^{2} + 430 a - 22597\) , \( 152084 a^{2} + 22769 a - 1190504\bigr] \) |
${y}^2+\left(a^{2}-5\right){y}={x}^{3}+{x}^{2}+\left(2886a^{2}+430a-22597\right){x}+152084a^{2}+22769a-1190504$ |
| 15.2-b1 |
15.2-b |
$2$ |
$3$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{7} \cdot 5^{6} \) |
$4.97532$ |
$(-a+3), (a^2+a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.016887930$ |
$52.77265123$ |
3.167292992 |
\( \frac{825621512192}{34171875} a^{2} + \frac{136621490176}{34171875} a - \frac{6558260396032}{34171875} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 61 a^{2} + 2 a - 493\) , \( -495 a^{2} - 50 a + 3946\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(61a^{2}+2a-493\right){x}-495a^{2}-50a+3946$ |
| 15.2-b2 |
15.2-b |
$2$ |
$3$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{21} \cdot 5^{2} \) |
$4.97532$ |
$(-a+3), (a^2+a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.050663790$ |
$17.59088374$ |
3.167292992 |
\( \frac{16617904504832}{261508830075} a^{2} - \frac{17777360175104}{261508830075} a + \frac{188962230960128}{261508830075} \) |
\( \bigl[0\) , \( -a^{2} + a + 7\) , \( a^{2} + a - 6\) , \( -11 a + 32\) , \( -4 a^{2} + 26\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-11a+32\right){x}-4a^{2}+26$ |
| 24.1-a1 |
24.1-a |
$4$ |
$4$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{3} \cdot 3 \) |
$5.38073$ |
$(-a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$3.901585749$ |
$3.476287946$ |
4.590611139 |
\( \frac{3199357281992850301448}{3} a^{2} + \frac{11031105496984479329279}{6} a - \frac{10570732553556537991018}{3} \) |
\( \bigl[a^{2} - 5\) , \( a\) , \( a^{2} + a - 6\) , \( -619 a^{2} + 2428 a - 2046\) , \( -28708 a^{2} + 111067 a - 89619\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+a{x}^{2}+\left(-619a^{2}+2428a-2046\right){x}-28708a^{2}+111067a-89619$ |
| 24.1-a2 |
24.1-a |
$4$ |
$4$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$5.38073$ |
$(-a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$0.975396437$ |
$13.90515178$ |
4.590611139 |
\( -\frac{5968930573744778728727048}{3} a^{2} - \frac{1787616069244446574537727}{6} a + \frac{46723794689882035726758106}{3} \) |
\( \bigl[a^{2} - 5\) , \( a\) , \( a^{2} + a - 6\) , \( 241 a^{2} - 192 a - 1266\) , \( -4280 a^{2} + 7931 a + 10149\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+a{x}^{2}+\left(241a^{2}-192a-1266\right){x}-4280a^{2}+7931a+10149$ |
| 24.1-a3 |
24.1-a |
$4$ |
$4$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{6} \cdot 3^{2} \) |
$5.38073$ |
$(-a+3), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1.950792874$ |
$27.81030357$ |
4.590611139 |
\( -\frac{19781092638623}{36} a^{2} - \frac{584659501150}{9} a + \frac{39158677248844}{9} \) |
\( \bigl[a^{2} - 5\) , \( a\) , \( a^{2} + a - 6\) , \( -29 a^{2} + 158 a - 216\) , \( -438 a^{2} + 1611 a - 1143\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+a{x}^{2}+\left(-29a^{2}+158a-216\right){x}-438a^{2}+1611a-1143$ |
| 24.1-a4 |
24.1-a |
$4$ |
$4$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$5.38073$ |
$(-a+3), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.975396437$ |
$55.62060714$ |
4.590611139 |
\( \frac{340118329}{1296} a^{2} - \frac{22704961}{1296} a - \frac{2864359769}{1296} \) |
\( \bigl[a^{2} - 5\) , \( a\) , \( a^{2} + a - 6\) , \( -9 a^{2} + 38 a - 36\) , \( 50 a^{2} - 193 a + 153\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+a{x}^{2}+\left(-9a^{2}+38a-36\right){x}+50a^{2}-193a+153$ |
| 24.1-b1 |
24.1-b |
$4$ |
$4$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$5.38073$ |
$(-a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$3.388541664$ |
$3.043154790$ |
3.490201337 |
\( -\frac{5968930573744778728727048}{3} a^{2} - \frac{1787616069244446574537727}{6} a + \frac{46723794689882035726758106}{3} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} - a - 6\) , \( a\) , \( 8231 a^{2} + 1216 a - 64384\) , \( 711310 a^{2} + 106635 a - 5568343\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(8231a^{2}+1216a-64384\right){x}+711310a^{2}+106635a-5568343$ |
| 24.1-b2 |
24.1-b |
$4$ |
$4$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{3} \cdot 3 \) |
$5.38073$ |
$(-a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$0.847135416$ |
$12.17261916$ |
3.490201337 |
\( \frac{3199357281992850301448}{3} a^{2} + \frac{11031105496984479329279}{6} a - \frac{10570732553556537991018}{3} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} - a - 6\) , \( a\) , \( 471 a^{2} + 236 a - 4144\) , \( 10002 a^{2} + 3775 a - 84499\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(471a^{2}+236a-4144\right){x}+10002a^{2}+3775a-84499$ |
| 24.1-b3 |
24.1-b |
$4$ |
$4$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{6} \cdot 3^{2} \) |
$5.38073$ |
$(-a+3), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1.694270832$ |
$24.34523832$ |
3.490201337 |
\( -\frac{19781092638623}{36} a^{2} - \frac{584659501150}{9} a + \frac{39158677248844}{9} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} - a - 6\) , \( a\) , \( 511 a^{2} + 86 a - 4024\) , \( 10560 a^{2} + 1629 a - 82789\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(511a^{2}+86a-4024\right){x}+10560a^{2}+1629a-82789$ |
| 24.1-b4 |
24.1-b |
$4$ |
$4$ |
3.3.1257.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$5.38073$ |
$(-a+3), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.847135416$ |
$48.69047665$ |
3.490201337 |
\( \frac{340118329}{1296} a^{2} - \frac{22704961}{1296} a - \frac{2864359769}{1296} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} - a - 6\) , \( a\) , \( 31 a^{2} + 6 a - 244\) , \( 132 a^{2} + 21 a - 1033\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(31a^{2}+6a-244\right){x}+132a^{2}+21a-1033$ |
*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.
