| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$2$ |
$2$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$10.48513$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$826.5407674$ |
1.761038534 |
\( -33385375 a^{3} + 98228208 a^{2} - 21678582 a - 31986152 \) |
\( \bigl[a^{3} - 5 a - 2\) , \( -a^{3} + 4 a + 1\) , \( a^{2} - 3\) , \( -9 a^{3} + 5 a^{2} + 45 a + 3\) , \( -14 a^{3} + 8 a^{2} + 67 a + 4\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-9a^{3}+5a^{2}+45a+3\right){x}-14a^{3}+8a^{2}+67a+4$ |
| 1.1-a2 |
1.1-a |
$2$ |
$2$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.48513$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$826.5407674$ |
1.761038534 |
\( -57219 a^{3} + 13058 a^{2} + 284938 a + 127756 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( -a^{3} + 5 a + 5\) , \( a^{2} + 2 a\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(-a^{3}+5a+5\right){x}+a^{2}+2a$ |
| 3.1-a1 |
3.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$12.02857$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1193.614233$ |
1.271565023 |
\( -\frac{1458376}{9} a^{3} + \frac{4215455}{9} a^{2} - \frac{244136}{3} a - \frac{1438505}{9} \) |
\( \bigl[a^{2} - 3\) , \( 1\) , \( a\) , \( -142 a^{3} + 211 a^{2} + 607 a - 578\) , \( 1290 a^{3} - 1921 a^{2} - 5510 a + 5275\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-142a^{3}+211a^{2}+607a-578\right){x}+1290a^{3}-1921a^{2}-5510a+5275$ |
| 3.1-a2 |
3.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$12.02857$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$149.2017792$ |
1.271565023 |
\( -\frac{1358726430787}{3} a^{3} + \frac{3936959004773}{3} a^{2} - 225724202912 a - \frac{1431909234707}{3} \) |
\( \bigl[a^{2} - 3\) , \( 1\) , \( a\) , \( 163 a^{3} - 244 a^{2} - 693 a + 667\) , \( 6877 a^{3} - 10242 a^{2} - 29371 a + 28118\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(163a^{3}-244a^{2}-693a+667\right){x}+6877a^{3}-10242a^{2}-29371a+28118$ |
| 3.1-a3 |
3.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$12.02857$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$298.4035584$ |
1.271565023 |
\( \frac{42449155}{9} a^{3} - \frac{63210302}{9} a^{2} - \frac{60444241}{3} a + \frac{173589569}{9} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 3\) , \( a^{3} - 4 a - 2\) , \( -7 a^{3} + 20 a^{2} - 2 a - 5\) , \( 9 a^{3} - 28 a^{2} + 9 a + 12\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-3\right){x}^{2}+\left(-7a^{3}+20a^{2}-2a-5\right){x}+9a^{3}-28a^{2}+9a+12$ |
| 3.1-a4 |
3.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{8} \) |
$12.02857$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$298.4035584$ |
1.271565023 |
\( \frac{1782872021261}{6561} a^{3} + \frac{2803899367646}{6561} a^{2} - \frac{603096383303}{2187} a - \frac{1347028741097}{6561} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 6 a + 1\) , \( a^{2} - a - 2\) , \( -5 a^{2} - 10 a - 2\) , \( -9 a^{3} - 14 a^{2} + 11 a + 7\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+6a+1\right){x}^{2}+\left(-5a^{2}-10a-2\right){x}-9a^{3}-14a^{2}+11a+7$ |
| 3.1-a5 |
3.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$12.02857$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1193.614233$ |
1.271565023 |
\( \frac{271301}{81} a^{3} + \frac{361541}{81} a^{2} - \frac{77816}{27} a + \frac{314665}{81} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 6 a + 1\) , \( a^{2} - a - 2\) , \( -5 a^{3} + 25 a + 13\) , \( -6 a^{3} + 31 a + 14\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+6a+1\right){x}^{2}+\left(-5a^{3}+25a+13\right){x}-6a^{3}+31a+14$ |
| 3.1-a6 |
3.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$12.02857$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$596.8071169$ |
1.271565023 |
\( \frac{54736855}{3} a^{3} - \frac{81507791}{3} a^{2} - 77939370 a + \frac{223831205}{3} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( -a^{3} + a^{2} + 3 a + 2\) , \( 4 a^{3} - a^{2} - 20 a - 9\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{3}+a^{2}+3a+2\right){x}+4a^{3}-a^{2}-20a-9$ |
| 4.2-a1 |
4.2-a |
$4$ |
$6$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{4} \) |
$12.46900$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$109.2730594$ |
0.465637210 |
\( \frac{16468097552291}{4} a^{3} + \frac{25318785671585}{4} a^{2} - \frac{9047737028775}{2} a - \frac{6490032415391}{2} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( -a^{3} + 6 a + 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -10 a^{3} - 2 a^{2} + 56 a + 26\) , \( -20 a^{3} + 4 a^{2} + 97 a + 43\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+6a+2\right){x}^{2}+\left(-10a^{3}-2a^{2}+56a+26\right){x}-20a^{3}+4a^{2}+97a+43$ |
| 4.2-a2 |
4.2-a |
$4$ |
$6$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$12.46900$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$109.2730594$ |
0.465637210 |
\( -\frac{3604823}{8} a^{3} - \frac{9385051}{16} a^{2} + \frac{920395}{2} a + \frac{2501273}{8} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( -a^{3} + 4 a + 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -50 a^{3} - 61 a^{2} + 91 a + 53\) , \( -461 a^{3} - 682 a^{2} + 569 a + 385\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+4a+3\right){x}^{2}+\left(-50a^{3}-61a^{2}+91a+53\right){x}-461a^{3}-682a^{2}+569a+385$ |
| 4.2-a3 |
4.2-a |
$4$ |
$6$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{12} \) |
$12.46900$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$109.2730594$ |
0.465637210 |
\( \frac{19728534024304649}{64} a^{3} - 459023900125219 a^{2} - \frac{42137232085717011}{32} a + \frac{10084340820436855}{8} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -11 a^{3} - 132 a^{2} + 548 a - 364\) , \( -2609 a^{3} + 6092 a^{2} + 3669 a - 5912\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-11a^{3}-132a^{2}+548a-364\right){x}-2609a^{3}+6092a^{2}+3669a-5912$ |
| 4.2-a4 |
4.2-a |
$4$ |
$6$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{24} \) |
$12.46900$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$109.2730594$ |
0.465637210 |
\( -\frac{31352051939}{4096} a^{3} + \frac{22513398273}{2048} a^{2} + \frac{67489348133}{2048} a - \frac{30048164813}{1024} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 4 a - 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -186 a^{3} + 278 a^{2} + 795 a - 760\) , \( -2351 a^{3} + 3500 a^{2} + 10041 a - 9615\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(-186a^{3}+278a^{2}+795a-760\right){x}-2351a^{3}+3500a^{2}+10041a-9615$ |
| 6.1-a1 |
6.1-a |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{3} \) |
$13.11725$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 1 \) |
$1$ |
$177.7071155$ |
1.514500388 |
\( -\frac{428335248667}{108} a^{3} + \frac{1241149486259}{108} a^{2} - \frac{71181406865}{36} a - \frac{112861601042}{27} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{2} - 2 a - 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 13 a^{3} + 21 a^{2} - 17 a - 12\) , \( -59 a^{3} - 90 a^{2} + 64 a + 44\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(13a^{3}+21a^{2}-17a-12\right){x}-59a^{3}-90a^{2}+64a+44$ |
| 6.1-a2 |
6.1-a |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{12} \cdot 3^{3} \) |
$13.11725$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$355.4142310$ |
1.514500388 |
\( \frac{170612605}{1728} a^{3} + \frac{137474777}{864} a^{2} - \frac{26271029}{288} a - \frac{123494017}{1728} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a\) , \( a^{2} - a - 3\) , \( -13 a^{3} - 19 a^{2} + 18 a + 12\) , \( -99 a^{3} - 151 a^{2} + 113 a + 80\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+a{x}^{2}+\left(-13a^{3}-19a^{2}+18a+12\right){x}-99a^{3}-151a^{2}+113a+80$ |
| 6.1-a3 |
6.1-a |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{12} \) |
$13.11725$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$355.4142310$ |
1.514500388 |
\( \frac{235106583234208385}{2125764} a^{3} - \frac{350097084343087009}{2125764} a^{2} - \frac{334768032126905069}{708588} a + \frac{240355010757561538}{531441} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a\) , \( a + 1\) , \( -31 a^{3} + 44 a^{2} + 140 a - 134\) , \( 141 a^{3} - 208 a^{2} - 609 a + 578\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-31a^{3}+44a^{2}+140a-134\right){x}+141a^{3}-208a^{2}-609a+578$ |
| 6.1-a4 |
6.1-a |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{6} \) |
$13.11725$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$710.8284621$ |
1.514500388 |
\( \frac{721434223}{5832} a^{3} - \frac{475606843}{2916} a^{2} - \frac{583558085}{972} a + \frac{3236499041}{5832} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a\) , \( a + 1\) , \( -a^{3} - a^{2} + 10 a - 4\) , \( 2 a^{3} - 5 a^{2} - 3 a + 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-a^{3}-a^{2}+10a-4\right){x}+2a^{3}-5a^{2}-3a+4$ |
| 6.1-b1 |
6.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3 \) |
$13.11725$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.347898544$ |
$822.9589825$ |
2.440031162 |
\( \frac{217346371092505}{6} a^{3} - \frac{323647972048847}{6} a^{2} - \frac{309479800438793}{2} a + \frac{444390878480629}{3} \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( 1\) , \( -32 a^{3} + 47 a^{2} + 133 a - 136\) , \( 157 a^{3} - 229 a^{2} - 672 a + 622\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(-32a^{3}+47a^{2}+133a-136\right){x}+157a^{3}-229a^{2}-672a+622$ |
| 6.1-b2 |
6.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3 \) |
$13.11725$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.347898544$ |
$822.9589825$ |
2.440031162 |
\( \frac{70023155}{6} a^{3} + \frac{107666327}{6} a^{2} - \frac{25635823}{2} a - \frac{27574669}{3} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 6 a + 2\) , \( a + 1\) , \( -9 a^{3} + 10 a^{2} + 36 a - 10\) , \( 3 a^{3} - 9 a^{2} - 8 a + 28\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+6a+2\right){x}^{2}+\left(-9a^{3}+10a^{2}+36a-10\right){x}+3a^{3}-9a^{2}-8a+28$ |
| 6.1-b3 |
6.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{3} \) |
$13.11725$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.115966181$ |
$822.9589825$ |
2.440031162 |
\( -\frac{33912732431669}{108} a^{3} + \frac{5112093918679}{108} a^{2} + \frac{57968401931615}{36} a + \frac{39932388022285}{54} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 5\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -3 a^{3} - 10 a^{2} + a + 9\) , \( -5 a^{3} - 2 a^{2} + 10 a - 3\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-5\right){x}^{2}+\left(-3a^{3}-10a^{2}+a+9\right){x}-5a^{3}-2a^{2}+10a-3$ |
| 6.1-b4 |
6.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{4} \cdot 3^{4} \) |
$13.11725$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.086974636$ |
$411.4794912$ |
2.440031162 |
\( -\frac{3222745}{324} a^{3} + \frac{4512739}{162} a^{2} - \frac{104917}{54} a - \frac{3847643}{324} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{2} - a - 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 2 a^{3} + a^{2} - 6 a - 2\) , \( -10 a^{3} - 16 a^{2} + 12 a + 6\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(2a^{3}+a^{2}-6a-2\right){x}-10a^{3}-16a^{2}+12a+6$ |
| 6.1-b5 |
6.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{2} \) |
$13.11725$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$0.173949272$ |
$1645.917965$ |
2.440031162 |
\( \frac{45355135}{18} a^{3} - \frac{33757039}{9} a^{2} - \frac{32282846}{3} a + \frac{185503295}{18} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a\) , \( 1\) , \( a^{3} - 3 a^{2} + a\) , \( 5 a^{3} - 4 a^{2} - 19 a - 8\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(a^{3}-3a^{2}+a\right){x}+5a^{3}-4a^{2}-19a-8$ |
| 6.1-b6 |
6.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{12} \cdot 3^{12} \) |
$13.11725$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.028991545$ |
$411.4794912$ |
2.440031162 |
\( -\frac{29415558493}{34012224} a^{3} + \frac{52474467157}{17006112} a^{2} - \frac{11747336173}{5668704} a - \frac{17859045011}{34012224} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{3} - 4 a - 2\) , \( 2 a^{3} - 6 a^{2} + 3 a + 4\) , \( -4 a^{3} + 11 a^{2} - 2 a - 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(2a^{3}-6a^{2}+3a+4\right){x}-4a^{3}+11a^{2}-2a-4$ |
| 6.1-b7 |
6.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{3} \) |
$13.11725$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.115966181$ |
$822.9589825$ |
2.440031162 |
\( -\frac{942982319902575955}{108} a^{3} + \frac{2732397954729249233}{108} a^{2} - \frac{156706278353107823}{36} a - \frac{496931168195378821}{54} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -486 a^{3} + 721 a^{2} + 2081 a - 1991\) , \( 9570 a^{3} - 14248 a^{2} - 40889 a + 39139\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-486a^{3}+721a^{2}+2081a-1991\right){x}+9570a^{3}-14248a^{2}-40889a+39139$ |
| 6.1-b8 |
6.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{6} \) |
$13.11725$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.057983090$ |
$1645.917965$ |
2.440031162 |
\( -\frac{132813262385}{5832} a^{3} + \frac{95367546271}{1458} a^{2} - \frac{2455099088}{243} a - \frac{135594053005}{5832} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -61 a^{3} + 91 a^{2} + 261 a - 251\) , \( -231 a^{3} + 344 a^{2} + 987 a - 945\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-61a^{3}+91a^{2}+261a-251\right){x}-231a^{3}+344a^{2}+987a-945$ |
| 6.1-c1 |
6.1-c |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{4} \) |
$13.11725$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$140.3070780$ |
0.597880179 |
\( -\frac{33750060308977022999}{162} a^{3} + \frac{5087616625611641191}{162} a^{2} + \frac{57690330287187031601}{54} a + \frac{39740734720421590732}{81} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -160 a^{3} + 239 a^{2} + 685 a - 654\) , \( 1542 a^{3} - 2291 a^{2} - 6590 a + 6286\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-160a^{3}+239a^{2}+685a-654\right){x}+1542a^{3}-2291a^{2}-6590a+6286$ |
| 6.1-c2 |
6.1-c |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{2} \) |
$13.11725$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$280.6141560$ |
0.597880179 |
\( -\frac{3297848369}{18} a^{3} + \frac{248643980}{9} a^{2} + \frac{2818603117}{3} a + \frac{7766572349}{18} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -30 a^{3} + 44 a^{2} + 130 a - 114\) , \( -169 a^{3} + 251 a^{2} + 724 a - 686\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-30a^{3}+44a^{2}+130a-114\right){x}-169a^{3}+251a^{2}+724a-686$ |
| 6.1-c3 |
6.1-c |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3 \) |
$13.11725$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$70.15353902$ |
0.597880179 |
\( -\frac{105910775}{6} a^{3} + \frac{325875235}{6} a^{2} - \frac{38995627}{2} a - \frac{35503580}{3} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 4 a - 1\) , \( a^{2} - 2\) , \( 4 a^{3} - a^{2} - 17 a - 6\) , \( 6 a^{3} - a^{2} - 29 a - 14\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(4a^{3}-a^{2}-17a-6\right){x}+6a^{3}-a^{2}-29a-14$ |
| 6.1-c4 |
6.1-c |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3 \) |
$13.11725$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$140.3070780$ |
0.597880179 |
\( \frac{4197994945}{12} a^{3} + \frac{3227146547}{6} a^{2} - \frac{768762653}{2} a - \frac{3308726449}{12} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 0\) , \( 17 a^{3} - 3 a^{2} - 87 a - 35\) , \( 61 a^{3} - 10 a^{2} - 312 a - 141\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(17a^{3}-3a^{2}-87a-35\right){x}+61a^{3}-10a^{2}-312a-141$ |
| 6.1-d1 |
6.1-d |
$2$ |
$2$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{3} \) |
$13.11725$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$0.057143165$ |
$1699.726884$ |
2.483300439 |
\( -\frac{63543155}{108} a^{3} + \frac{9983509}{108} a^{2} + \frac{109272449}{36} a + \frac{75979981}{54} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2\) , \( a\) , \( -5 a^{3} + 10 a^{2} + 21 a - 30\) , \( -16 a^{3} + 22 a^{2} + 70 a - 56\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-5a^{3}+10a^{2}+21a-30\right){x}-16a^{3}+22a^{2}+70a-56$ |
| 6.1-d2 |
6.1-d |
$2$ |
$2$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3^{6} \) |
$13.11725$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.028571582$ |
$849.8634420$ |
2.483300439 |
\( -\frac{732365}{5832} a^{3} + \frac{690602}{729} a^{2} - \frac{624997}{486} a - \frac{4595629}{5832} \) |
\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{3} - 4 a - 1\) , \( -a^{2} + 4\) , \( -2 a^{3} + 7 a^{2} - 5 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+3\right){x}^{2}+\left(-a^{2}+4\right){x}-2a^{3}+7a^{2}-5a-3$ |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$13.59754$ |
$(-a), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.676563348$ |
$48.40157157$ |
2.232659468 |
\( -20940718080 a^{3} + \frac{6309019649}{2} a^{2} + 107388338175 a + \frac{98663400961}{2} \) |
\( \bigl[a^{2} - 3\) , \( -a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 86 a^{3} - 109 a^{2} - 667 a - 282\) , \( 881 a^{3} - 1467 a^{2} - 7702 a - 3314\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(86a^{3}-109a^{2}-667a-282\right){x}+881a^{3}-1467a^{2}-7702a-3314$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$13.59754$ |
$(-a), (a^2+a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.169140837$ |
$774.4251451$ |
2.232659468 |
\( -\frac{89091}{16} a^{3} + \frac{249965}{16} a^{2} - \frac{13717}{8} a - \frac{37319}{8} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 7 a^{3} - 14 a^{2} - 17 a + 21\) , \( -8 a^{3} + 27 a^{2} - 16 a - 1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+5\right){x}^{2}+\left(7a^{3}-14a^{2}-17a+21\right){x}-8a^{3}+27a^{2}-16a-1$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$13.59754$ |
$(-a), (a^2+a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.338281674$ |
$774.4251451$ |
2.232659468 |
\( -\frac{229379}{4} a^{3} + \frac{32875}{4} a^{2} + \frac{589725}{2} a + \frac{560223}{4} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - 5 a - 2\) , \( -24 a^{3} + 34 a^{2} + 110 a - 108\) , \( -144 a^{3} + 217 a^{2} + 608 a - 588\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-24a^{3}+34a^{2}+110a-108\right){x}-144a^{3}+217a^{2}+608a-588$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$13.59754$ |
$(-a), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.169140837$ |
$774.4251451$ |
2.232659468 |
\( \frac{54439}{16} a^{3} - \frac{21433}{8} a^{2} - \frac{101045}{8} a + \frac{167141}{16} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( a^{2} - 3\) , \( -5 a^{3} + 6 a^{2} + 20 a - 8\) , \( -3 a^{2} + 3 a + 10\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+4\right){x}^{2}+\left(-5a^{3}+6a^{2}+20a-8\right){x}-3a^{2}+3a+10$ |
| 9.1-a1 |
9.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{14} \) |
$13.79921$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.636644725$ |
$132.0959631$ |
2.866891478 |
\( \frac{1782872021261}{6561} a^{3} + \frac{2803899367646}{6561} a^{2} - \frac{603096383303}{2187} a - \frac{1347028741097}{6561} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 5 a - 2\) , \( a^{2} - 3\) , \( -572 a^{3} - 879 a^{2} + 630 a + 452\) , \( 24169 a^{3} + 37159 a^{2} - 26558 a - 19053\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(-572a^{3}-879a^{2}+630a+452\right){x}+24169a^{3}+37159a^{2}-26558a-19053$ |
| 9.1-a2 |
9.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$13.79921$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.318322362$ |
$1056.767705$ |
2.866891478 |
\( \frac{271301}{81} a^{3} + \frac{361541}{81} a^{2} - \frac{77816}{27} a + \frac{314665}{81} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 3\) , \( 4 a^{3} - 9 a^{2} - 10 a + 9\) , \( -3 a^{3} + 10 a^{2} - 5 a - 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(4a^{3}-9a^{2}-10a+9\right){x}-3a^{3}+10a^{2}-5a-3$ |
| 9.1-a3 |
9.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{7} \) |
$13.79921$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.318322362$ |
$528.3838525$ |
2.866891478 |
\( -\frac{1358726430787}{3} a^{3} + \frac{3936959004773}{3} a^{2} - 225724202912 a - \frac{1431909234707}{3} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 41 a^{3} - 14 a^{2} - 196 a - 83\) , \( -267 a^{3} + 50 a^{2} + 1346 a + 624\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(41a^{3}-14a^{2}-196a-83\right){x}-267a^{3}+50a^{2}+1346a+624$ |
| 9.1-a4 |
9.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$13.79921$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.159161181$ |
$2113.535410$ |
2.866891478 |
\( -\frac{1458376}{9} a^{3} + \frac{4215455}{9} a^{2} - \frac{244136}{3} a - \frac{1438505}{9} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{3} + a^{2} - 6 a - 8\) , \( -5 a^{3} + 26 a + 15\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(a^{3}+a^{2}-6a-8\right){x}-5a^{3}+26a+15$ |
| 9.1-a5 |
9.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{7} \) |
$13.79921$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.079580590$ |
$1056.767705$ |
2.866891478 |
\( \frac{54736855}{3} a^{3} - \frac{81507791}{3} a^{2} - 77939370 a + \frac{223831205}{3} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( a^{3} - 4 a - 1\) , \( -2 a^{3} + 4 a^{2} + 6 a - 3\) , \( 4 a^{3} - 6 a^{2} - 22 a + 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-4\right){x}^{2}+\left(-2a^{3}+4a^{2}+6a-3\right){x}+4a^{3}-6a^{2}-22a+17$ |
| 9.1-a6 |
9.1-a |
$6$ |
$8$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$13.79921$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.636644725$ |
$264.1919262$ |
2.866891478 |
\( \frac{42449155}{9} a^{3} - \frac{63210302}{9} a^{2} - \frac{60444241}{3} a + \frac{173589569}{9} \) |
\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -a^{2} + 4\) , \( -4 a^{3} + 6 a^{2} + 17 a - 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(-a^{2}+4\right){x}-4a^{3}+6a^{2}+17a-17$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$13.79921$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$0.411116267$ |
$190.3218305$ |
1.333668321 |
\( -33385375 a^{3} + 98228208 a^{2} - 21678582 a - 31986152 \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 5 a^{3} - 3 a^{2} - 22 a - 8\) , \( -46 a^{3} + 6 a^{2} + 238 a + 108\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(5a^{3}-3a^{2}-22a-8\right){x}-46a^{3}+6a^{2}+238a+108$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.79921$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$0.205558133$ |
$380.6436611$ |
1.333668321 |
\( -57219 a^{3} + 13058 a^{2} + 284938 a + 127756 \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - 4 a - 1\) , \( 3 a^{3} + 7 a^{2} - 2 a - 2\) , \( -129 a^{3} - 200 a^{2} + 140 a + 101\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(3a^{3}+7a^{2}-2a-2\right){x}-129a^{3}-200a^{2}+140a+101$ |
| 12.1-a1 |
12.1-a |
$2$ |
$2$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{8} \) |
$14.30447$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$185.2369804$ |
3.157346603 |
\( -\frac{3788866415}{6561} a^{3} + \frac{10540665442}{6561} a^{2} - \frac{330582970}{2187} a - \frac{3449696932}{6561} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - a - 2\) , \( 2 a^{3} - a^{2} - 10 a - 2\) , \( -10 a^{3} - 16 a^{2} + 11 a + 7\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(2a^{3}-a^{2}-10a-2\right){x}-10a^{3}-16a^{2}+11a+7$ |
| 12.1-a2 |
12.1-a |
$2$ |
$2$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{16} \) |
$14.30447$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$92.61849022$ |
3.157346603 |
\( \frac{334042690739}{43046721} a^{3} - \frac{202915825810}{43046721} a^{2} - \frac{360317063630}{14348907} a + \frac{858784027156}{43046721} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( 4 a^{3} - 2 a^{2} - 24 a - 9\) , \( -89 a^{3} + 12 a^{2} + 452 a + 206\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(4a^{3}-2a^{2}-24a-9\right){x}-89a^{3}+12a^{2}+452a+206$ |
| 12.1-b1 |
12.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{4} \) |
$14.30447$ |
$(-a), (a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$309.7102124$ |
1.979617848 |
\( \frac{15914}{81} a^{3} - \frac{9523}{81} a^{2} - \frac{1052}{27} a + \frac{138142}{81} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - a - 2\) , \( a^{3} - 5 a - 2\) , \( -3 a - 1\) , \( -a^{3} - a^{2} + 2 a + 1\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-3a-1\right){x}-a^{3}-a^{2}+2a+1$ |
| 12.1-b2 |
12.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{6} \) |
$14.30447$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$619.4204248$ |
1.979617848 |
\( \frac{38193011594}{729} a^{3} - \frac{71074511599}{729} a^{2} - \frac{51361057400}{243} a + \frac{224617191322}{729} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{3} - 5 a - 1\) , \( 0\) , \( -22 a^{3} - 33 a^{2} + 28 a + 17\) , \( 72 a^{3} + 113 a^{2} - 77 a - 59\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(-22a^{3}-33a^{2}+28a+17\right){x}+72a^{3}+113a^{2}-77a-59$ |
| 12.1-b3 |
12.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{3} \) |
$14.30447$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$309.7102124$ |
1.979617848 |
\( -\frac{35543392331765509}{27} a^{3} + \frac{5358020598900419}{27} a^{2} + \frac{60755696726720026}{9} a + \frac{83704683519399082}{27} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{3} - 5 a - 1\) , \( 0\) , \( -157 a^{3} - 263 a^{2} + 183 a + 132\) , \( -3899 a^{3} - 5921 a^{2} + 4260 a + 3041\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(-157a^{3}-263a^{2}+183a+132\right){x}-3899a^{3}-5921a^{2}+4260a+3041$ |
| 12.1-b4 |
12.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3 \) |
$14.30447$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$309.7102124$ |
1.979617848 |
\( \frac{14822658932714}{3} a^{3} + \frac{22789015289915}{3} a^{2} - 5429144305668 a - \frac{11683138877174}{3} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( -a^{3} + 5 a + 1\) , \( a^{2} - a - 2\) , \( -57 a^{3} + 72 a^{2} + 255 a - 187\) , \( 337 a^{3} - 515 a^{2} - 1440 a + 1460\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-57a^{3}+72a^{2}+255a-187\right){x}+337a^{3}-515a^{2}-1440a+1460$ |
| 12.1-b5 |
12.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$14.30447$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 3 \) |
$1$ |
$77.42755310$ |
1.979617848 |
\( -\frac{98626994}{3} a^{3} + \frac{285623137}{3} a^{2} - 16456032 a - \frac{102425494}{3} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( -a^{2} + a + 2\) , \( a^{3} - 4 a - 2\) , \( -37 a^{3} - 54 a^{2} + 46 a + 31\) , \( -526 a^{3} - 806 a^{2} + 585 a + 417\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-37a^{3}-54a^{2}+46a+31\right){x}-526a^{3}-806a^{2}+585a+417$ |
| 12.1-b6 |
12.1-b |
$8$ |
$12$ |
4.4.13768.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{12} \) |
$14.30447$ |
$(-a), (a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$309.7102124$ |
1.979617848 |
\( \frac{52753233221}{531441} a^{3} + \frac{85136921753}{531441} a^{2} - \frac{18478786658}{177147} a - \frac{51304263530}{531441} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 3 a\) , \( a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - a - 1\) , \( -6 a^{3} + 17 a^{2} - 2 a - 7\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a\right){x}^{2}+\left(a^{3}-2a^{2}-a-1\right){x}-6a^{3}+17a^{2}-2a-7$ |
*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.
