| 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 |
| 5.1-a1 |
5.1-a |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{9} \) |
$5.14278$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$1$ |
$17.69755109$ |
3.619019090 |
\( -\frac{10186959944153468}{1953125} a^{2} + \frac{11483339371396431}{1953125} a + \frac{80033451487759023}{1953125} \) |
\( \bigl[a\) , \( a\) , \( a^{2} - a - 5\) , \( 19 a^{2} - 29 a - 116\) , \( -78 a^{2} + 131 a + 471\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+a{x}^{2}+\left(19a^{2}-29a-116\right){x}-78a^{2}+131a+471$ |
| 5.1-a2 |
5.1-a |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{3} \) |
$5.14278$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$53.09265329$ |
3.619019090 |
\( -\frac{3414383}{125} a^{2} + \frac{11109861}{125} a + \frac{1997838}{125} \) |
\( \bigl[a\) , \( a\) , \( a^{2} - a - 5\) , \( -a^{2} + 6 a - 1\) , \( -2 a^{2} + 10 a - 4\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+a{x}^{2}+\left(-a^{2}+6a-1\right){x}-2a^{2}+10a-4$ |
| 5.1-b1 |
5.1-b |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{9} \) |
$5.14278$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$4.828797984$ |
$6.144234086$ |
2.022382201 |
\( -\frac{10186959944153468}{1953125} a^{2} + \frac{11483339371396431}{1953125} a + \frac{80033451487759023}{1953125} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 139 a^{2} - 164 a - 1101\) , \( 1825 a^{2} - 2137 a - 14517\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(139a^{2}-164a-1101\right){x}+1825a^{2}-2137a-14517$ |
| 5.1-b2 |
5.1-b |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{3} \) |
$5.14278$ |
$(a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.609599328$ |
$165.8943203$ |
2.022382201 |
\( -\frac{3414383}{125} a^{2} + \frac{11109861}{125} a + \frac{1997838}{125} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 4 a^{2} + a - 11\) , \( 6 a^{2} + 2 a - 23\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(4a^{2}+a-11\right){x}+6a^{2}+2a-23$ |
| 9.2-a1 |
9.2-a |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$56.96372128$ |
2.588591603 |
\( -\frac{80}{9} a^{2} + 8 a + \frac{703}{9} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - a - 5\) , \( -2 a + 7\) , \( -2 a^{2} - 3 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-2a+7\right){x}-2a^{2}-3a-4$ |
| 9.2-b1 |
9.2-b |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{24} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$3.321575189$ |
1.358475413 |
\( -\frac{15972897045786395}{387420489} a^{2} + \frac{5848363495354835}{43046721} a + \frac{6954423430456138}{387420489} \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 5\) , \( 1\) , \( -839863 a^{2} + 2767690 a + 365912\) , \( -1043276476 a^{2} + 3438029697 a + 454504390\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-839863a^{2}+2767690a+365912\right){x}-1043276476a^{2}+3438029697a+454504390$ |
| 9.2-b2 |
9.2-b |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$9$ |
\( 2 \) |
$1$ |
$29.89417670$ |
1.358475413 |
\( -\frac{948204140323028}{729} a^{2} - \frac{255245871679837}{81} a - \frac{277034073347147}{729} \) |
\( \bigl[1\) , \( a^{2} - 5\) , \( a + 1\) , \( -56 a^{2} + 185 a + 32\) , \( -1535 a^{2} + 5060 a + 664\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-56a^{2}+185a+32\right){x}-1535a^{2}+5060a+664$ |
| 9.2-c1 |
9.2-c |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$62.70470109$ |
2.849477862 |
\( -\frac{948204140323028}{729} a^{2} - \frac{255245871679837}{81} a - \frac{277034073347147}{729} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 6\) , \( a^{2} - 5\) , \( -37 a^{2} - 77 a + 18\) , \( 207 a^{2} + 522 a + 108\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-37a^{2}-77a+18\right){x}+207a^{2}+522a+108$ |
| 9.2-c2 |
9.2-c |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{24} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$62.70470109$ |
2.849477862 |
\( -\frac{15972897045786395}{387420489} a^{2} + \frac{5848363495354835}{43046721} a + \frac{6954423430456138}{387420489} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 6\) , \( 1\) , \( -589 a^{2} + 1939 a + 262\) , \( 18356 a^{2} - 60493 a - 7989\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-589a^{2}+1939a+262\right){x}+18356a^{2}-60493a-7989$ |
| 9.2-d1 |
9.2-d |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$53.51551912$ |
2.431895605 |
\( -\frac{80}{9} a^{2} + 8 a + \frac{703}{9} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 6\) , \( 1\) , \( a^{2} - 16 a + 50\) , \( -322 a^{2} + 1044 a + 205\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(a^{2}-16a+50\right){x}-322a^{2}+1044a+205$ |
| 9.2-e1 |
9.2-e |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{9} \) |
$5.67210$ |
$(a+2)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.512577807$ |
$154.7431697$ |
3.604428981 |
\( \frac{18601897}{27} a^{2} - \frac{2331535}{3} a - \frac{146056838}{27} \) |
\( \bigl[a^{2} - 4\) , \( 0\) , \( a + 1\) , \( 7 a^{2} + 17 a + 3\) , \( 21 a^{2} + 51 a + 6\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(7a^{2}+17a+3\right){x}+21a^{2}+51a+6$ |
| 9.2-e2 |
9.2-e |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{15} \) |
$5.67210$ |
$(a+2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.512577807$ |
$17.19368553$ |
3.604428981 |
\( \frac{2839789903}{19683} a^{2} - \frac{1059467056}{2187} a - \frac{1259589011}{19683} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -4 a^{2} + 14 a + 7\) , \( -18 a^{2} + 61 a + 6\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-4a^{2}+14a+7\right){x}-18a^{2}+61a+6$ |
| 9.2-f1 |
9.2-f |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{9} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$23.99850874$ |
2.181119379 |
\( \frac{18601897}{27} a^{2} - \frac{2331535}{3} a - \frac{146056838}{27} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + a + 5\) , \( 0\) , \( 630 a^{2} + 1517 a + 163\) , \( -10590 a^{2} - 25811 a - 3449\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(630a^{2}+1517a+163\right){x}-10590a^{2}-25811a-3449$ |
| 9.2-f2 |
9.2-f |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{15} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$23.99850874$ |
2.181119379 |
\( \frac{2839789903}{19683} a^{2} - \frac{1059467056}{2187} a - \frac{1259589011}{19683} \) |
\( \bigl[a^{2} - 5\) , \( a + 1\) , \( a + 1\) , \( -12 a^{2} - 20 a + 18\) , \( -141 a^{2} - 340 a - 38\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-12a^{2}-20a+18\right){x}-141a^{2}-340a-38$ |
| 9.2-g1 |
9.2-g |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$9$ |
\( 2 \) |
$1$ |
$159.7263401$ |
1.814603460 |
\( 16777217 a^{2} + 196607 a + 760 \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 5\) , \( a^{2} - a - 4\) , \( 2 a^{2} - 2 a - 29\) , \( 30 a^{2} - 35 a - 235\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(2a^{2}-2a-29\right){x}+30a^{2}-35a-235$ |
| 9.2-g2 |
9.2-g |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$9$ |
\( 2 \) |
$1$ |
$159.7263401$ |
1.814603460 |
\( 40 a^{2} + 4057 a + 447 \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 5\) , \( a^{2} - a - 4\) , \( -3 a^{2} + 3 a + 16\) , \( -2 a^{2} + 2 a + 12\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-3a^{2}+3a+16\right){x}-2a^{2}+2a+12$ |
| 9.2-g3 |
9.2-g |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$17.74737113$ |
1.814603460 |
\( -1953025202388974 a^{2} + 2201611873026121 a + 15343974121341705 \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 4\) , \( -88 a^{2} + 368 a - 241\) , \( -205 a^{2} + 1085 a - 1325\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-88a^{2}+368a-241\right){x}-205a^{2}+1085a-1325$ |
| 9.2-g4 |
9.2-g |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$17.74737113$ |
1.814603460 |
\( 15941405 a^{2} - 17928106 a - 125144951 \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 4\) , \( 32 a^{2} - 107 a - 21\) , \( 18 a^{2} - 61 a - 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(32a^{2}-107a-21\right){x}+18a^{2}-61a-15$ |
| 9.2-h1 |
9.2-h |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$108.4182891$ |
1.231707947 |
\( 16777217 a^{2} + 196607 a + 760 \) |
\( \bigl[a\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 4\) , \( 29 a^{2} - 134 a - 450\) , \( -341 a^{2} + 1207 a + 4572\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(29a^{2}-134a-450\right){x}-341a^{2}+1207a+4572$ |
| 9.2-h2 |
9.2-h |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$108.4182891$ |
1.231707947 |
\( 40 a^{2} + 4057 a + 447 \) |
\( \bigl[a\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 4\) , \( -a^{2} - 9 a - 5\) , \( -14 a^{2} + 22 a + 129\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-a^{2}-9a-5\right){x}-14a^{2}+22a+129$ |
| 9.2-h3 |
9.2-h |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$108.4182891$ |
1.231707947 |
\( -1953025202388974 a^{2} + 2201611873026121 a + 15343974121341705 \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 379 a^{2} - 427 a - 2976\) , \( -7825 a^{2} + 8821 a + 61477\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(379a^{2}-427a-2976\right){x}-7825a^{2}+8821a+61477$ |
| 9.2-h4 |
9.2-h |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$5.67210$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$108.4182891$ |
1.231707947 |
\( 15941405 a^{2} - 17928106 a - 125144951 \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 24 a^{2} - 27 a - 186\) , \( -120 a^{2} + 135 a + 943\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(24a^{2}-27a-186\right){x}-120a^{2}+135a+943$ |
| 15.1-a1 |
15.1-a |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5 \) |
$6.17616$ |
$(a+2), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$6.517648677$ |
$0.624151145$ |
4.991253964 |
\( -\frac{46391660173305545767423}{45} a^{2} + \frac{16986645153177195186489}{5} a + \frac{20210570005476058193738}{45} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 2 a - 5\) , \( a^{2} - a - 5\) , \( -392 a^{2} - 1270 a - 843\) , \( -20255 a^{2} - 48959 a - 5658\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-392a^{2}-1270a-843\right){x}-20255a^{2}-48959a-5658$ |
| 15.1-a2 |
15.1-a |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{3} \) |
$6.17616$ |
$(a+2), (a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$2.172549559$ |
$16.85208092$ |
4.991253964 |
\( -\frac{2982248281408}{91125} a^{2} + \frac{414935673379}{10125} a + \frac{22154828213363}{91125} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 2 a - 5\) , \( a^{2} - a - 5\) , \( 63 a^{2} - 80 a - 508\) , \( -559 a^{2} + 430 a + 3935\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(63a^{2}-80a-508\right){x}-559a^{2}+430a+3935$ |
| 15.1-b1 |
15.1-b |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{3} \) |
$6.17616$ |
$(a+2), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.697849448$ |
$29.65349310$ |
2.821136105 |
\( -\frac{2982248281408}{91125} a^{2} + \frac{414935673379}{10125} a + \frac{22154828213363}{91125} \) |
\( \bigl[a\) , \( a\) , \( a^{2} - a - 4\) , \( 6 a^{2} - 4 a - 51\) , \( 20 a^{2} - 26 a - 142\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+a{x}^{2}+\left(6a^{2}-4a-51\right){x}+20a^{2}-26a-142$ |
| 15.1-b2 |
15.1-b |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5 \) |
$6.17616$ |
$(a+2), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$2.093548345$ |
$9.884497702$ |
2.821136105 |
\( -\frac{46391660173305545767423}{45} a^{2} + \frac{16986645153177195186489}{5} a + \frac{20210570005476058193738}{45} \) |
\( \bigl[a\) , \( a\) , \( a^{2} - a - 4\) , \( -89 a^{2} + 296 a - 31\) , \( 1281 a^{2} - 4313 a - 590\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+a{x}^{2}+\left(-89a^{2}+296a-31\right){x}+1281a^{2}-4313a-590$ |
| 19.1-a1 |
19.1-a |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{2} \) |
$6.42435$ |
$(a^2-2a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$112.9761721$ |
5.133954807 |
\( -\frac{446172759}{361} a^{2} + \frac{1470396303}{361} a + \frac{194318006}{361} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( 0\) , \( 2 a + 7\) , \( 2 a^{2} + 3 a - 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(2a+7\right){x}+2a^{2}+3a-3$ |
| 19.1-b1 |
19.1-b |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{2} \) |
$6.42435$ |
$(a^2-2a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.529055838$ |
$44.57873040$ |
3.215256665 |
\( -\frac{446172759}{361} a^{2} + \frac{1470396303}{361} a + \frac{194318006}{361} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{2} - a - 5\) , \( -26 a^{2} + 88 a + 14\) , \( -159 a^{2} + 529 a + 64\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-26a^{2}+88a+14\right){x}-159a^{2}+529a+64$ |
| 21.1-a1 |
21.1-a |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3 \cdot 7 \) |
$6.53241$ |
$(a+2), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.654115504$ |
$88.09424003$ |
3.927881719 |
\( -\frac{118784}{21} a^{2} + \frac{45056}{7} a + \frac{925696}{21} \) |
\( \bigl[0\) , \( -a\) , \( a^{2} - a - 5\) , \( 3 a^{2} - 3 a - 21\) , \( -4 a^{2} + 4 a + 29\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){y}={x}^{3}-a{x}^{2}+\left(3a^{2}-3a-21\right){x}-4a^{2}+4a+29$ |
| 21.1-b1 |
21.1-b |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3 \cdot 7 \) |
$6.53241$ |
$(a+2), (a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$115.4291203$ |
2.622711832 |
\( -\frac{118784}{21} a^{2} + \frac{45056}{7} a + \frac{925696}{21} \) |
\( \bigl[0\) , \( -a^{2} + 2 a + 6\) , \( a + 1\) , \( -8 a^{2} + 24 a + 12\) , \( 65 a^{2} - 216 a - 27\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-8a^{2}+24a+12\right){x}+65a^{2}-216a-27$ |
| 23.1-a1 |
23.1-a |
$2$ |
$2$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$6.63221$ |
$(-a^2+12)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$9.216347132$ |
6.950164663 |
\( \frac{301680929028200026577}{529} a^{2} + \frac{730881965203032303932}{529} a + \frac{88141248777783878212}{529} \) |
\( \bigl[a^{2} - 4\) , \( -a\) , \( a + 1\) , \( 3 a^{2} - 132 a - 315\) , \( -750 a^{2} - 1058 a + 1524\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(3a^{2}-132a-315\right){x}-750a^{2}-1058a+1524$ |
| 23.1-a2 |
23.1-a |
$2$ |
$2$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$6.63221$ |
$(-a^2+12)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 1 \) |
$1$ |
$36.86538852$ |
6.950164663 |
\( -\frac{257162332657}{23} a^{2} + \frac{276209193839}{23} a + \frac{1988986158735}{23} \) |
\( \bigl[a^{2} - 4\) , \( -a\) , \( a + 1\) , \( 38 a^{2} - 47 a - 305\) , \( -226 a^{2} + 210 a + 1673\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(38a^{2}-47a-305\right){x}-226a^{2}+210a+1673$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$6.63221$ |
$(-a^2+12)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$2.141082440$ |
2.118521310 |
\( \frac{301680929028200026577}{529} a^{2} + \frac{730881965203032303932}{529} a + \frac{88141248777783878212}{529} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( 0\) , \( 68 a^{2} - 212 a - 55\) , \( -156 a^{2} + 523 a + 38\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(68a^{2}-212a-55\right){x}-156a^{2}+523a+38$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$6.63221$ |
$(-a^2+12)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 1 \) |
$1$ |
$8.564329760$ |
2.118521310 |
\( -\frac{257162332657}{23} a^{2} + \frac{276209193839}{23} a + \frac{1988986158735}{23} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( 0\) , \( -12 a^{2} + 53 a - 20\) , \( -28 a^{2} + 106 a - 17\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-12a^{2}+53a-20\right){x}-28a^{2}+106a-17$ |
| 25.2-a1 |
25.2-a |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{7} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.215699522$ |
$86.41071411$ |
5.081983066 |
\( -\frac{317786}{5} a^{2} + \frac{360242}{5} a + \frac{2469581}{5} \) |
\( \bigl[a^{2} - a - 5\) , \( -a + 1\) , \( a\) , \( -11 a^{2} + 30 a + 20\) , \( -62 a^{2} + 200 a + 39\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a^{2}+30a+20\right){x}-62a^{2}+200a+39$ |
| 25.2-b1 |
25.2-b |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{7} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.254940919$ |
$85.28163853$ |
5.928045375 |
\( -\frac{792888}{5} a^{2} + \frac{893071}{5} a + \frac{6227643}{5} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( -a^{2} + 3 a + 11\) , \( a^{2} - 10 a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-a^{2}+3a+11\right){x}+a^{2}-10a-1$ |
| 25.2-c1 |
25.2-c |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{7} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.152935729$ |
$117.0241623$ |
2.439893895 |
\( -\frac{317786}{5} a^{2} + \frac{360242}{5} a + \frac{2469581}{5} \) |
\( \bigl[a^{2} - a - 4\) , \( 1\) , \( a^{2} - 4\) , \( -4 a^{2} - 12 a - 3\) , \( 10 a^{2} + 22 a\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+{x}^{2}+\left(-4a^{2}-12a-3\right){x}+10a^{2}+22a$ |
| 25.2-d1 |
25.2-d |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$6.406496359$ |
$27.62670039$ |
6.032204416 |
\( 16777217 a^{2} + 196607 a + 760 \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a\) , \( -368884 a^{2} - 893695 a - 107772\) , \( -389514333 a^{2} - 943675829 a - 113803280\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-368884a^{2}-893695a-107772\right){x}-389514333a^{2}-943675829a-113803280$ |
| 25.2-d2 |
25.2-d |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$3.203248179$ |
$55.25340078$ |
6.032204416 |
\( 40 a^{2} + 4057 a + 447 \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a\) , \( -23449 a^{2} - 56810 a - 6847\) , \( -5915121 a^{2} - 14330554 a - 1728202\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-23449a^{2}-56810a-6847\right){x}-5915121a^{2}-14330554a-1728202$ |
| 25.2-d3 |
25.2-d |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$2.135498786$ |
$82.88010118$ |
6.032204416 |
\( -1953025202388974 a^{2} + 2201611873026121 a + 15343974121341705 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 4\) , \( a\) , \( -606 a^{2} - 1467 a - 173\) , \( -1411 a^{2} - 3417 a - 411\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-606a^{2}-1467a-173\right){x}-1411a^{2}-3417a-411$ |
| 25.2-d4 |
25.2-d |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.067749393$ |
$165.7602023$ |
6.032204416 |
\( 15941405 a^{2} - 17928106 a - 125144951 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 4\) , \( a\) , \( -406 a^{2} - 982 a - 113\) , \( 14007 a^{2} + 33937 a + 4095\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-406a^{2}-982a-113\right){x}+14007a^{2}+33937a+4095$ |
| 25.2-e1 |
25.2-e |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{7} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.168819998$ |
$108.5426381$ |
2.498105102 |
\( -\frac{792888}{5} a^{2} + \frac{893071}{5} a + \frac{6227643}{5} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 5\) , \( 2 a^{2} - 8 a - 16\) , \( 10 a^{2} + 19 a\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(2a^{2}-8a-16\right){x}+10a^{2}+19a$ |
| 25.2-f1 |
25.2-f |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.632298327$ |
$40.70080592$ |
2.264274069 |
\( 16777217 a^{2} + 196607 a + 760 \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 6\) , \( 1\) , \( -2504 a^{2} - 6065 a - 729\) , \( -221458 a^{2} - 536526 a - 64703\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-2504a^{2}-6065a-729\right){x}-221458a^{2}-536526a-64703$ |
| 25.2-f2 |
25.2-f |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.816149163$ |
$81.40161184$ |
2.264274069 |
\( 40 a^{2} + 4057 a + 447 \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 6\) , \( 1\) , \( -159 a^{2} - 385 a - 44\) , \( -3538 a^{2} - 8572 a - 1034\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-159a^{2}-385a-44\right){x}-3538a^{2}-8572a-1034$ |
| 25.2-f3 |
25.2-f |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$2.448447490$ |
$27.13387061$ |
2.264274069 |
\( 15941405 a^{2} - 17928106 a - 125144951 \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 6\) , \( 0\) , \( 12 a^{2} - 38 a - 5\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(12a^{2}-38a-5\right){x}$ |
| 25.2-f4 |
25.2-f |
$4$ |
$6$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$6.72502$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$4.896894981$ |
$13.56693530$ |
2.264274069 |
\( -1953025202388974 a^{2} + 2201611873026121 a + 15343974121341705 \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 6\) , \( 0\) , \( -48 a^{2} + 152 a + 20\) , \( -89 a^{2} + 209 a + 28\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-48a^{2}+152a+20\right){x}-89a^{2}+209a+28$ |
| 27.1-a1 |
27.1-a |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{13} \) |
$6.81183$ |
$(a+2), (-a^2+3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$0.042990715$ |
$95.48019798$ |
5.595957724 |
\( -\frac{1331}{243} a^{2} - \frac{51013}{81} a + \frac{297259}{243} \) |
\( \bigl[1\) , \( a^{2} - a - 6\) , \( a^{2} - a - 4\) , \( -2 a^{2} + 2 a + 13\) , \( a^{2} - a - 11\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-2a^{2}+2a+13\right){x}+a^{2}-a-11$ |
| 27.1-b1 |
27.1-b |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{13} \) |
$6.81183$ |
$(a+2), (-a^2+3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.243177535$ |
$92.10560508$ |
3.053486139 |
\( -\frac{1331}{243} a^{2} - \frac{51013}{81} a + \frac{297259}{243} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -166 a^{2} + 548 a + 73\) , \( -1783 a^{2} + 5877 a + 777\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-166a^{2}+548a+73\right){x}-1783a^{2}+5877a+777$ |
| 31.1-a1 |
31.1-a |
$1$ |
$1$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$6.97050$ |
$(-a^2-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$4$ |
\( 1 \) |
$1$ |
$57.77079802$ |
5.250534877 |
\( -\frac{2847298}{31} a^{2} + \frac{8198152}{31} a + \frac{5411945}{31} \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( -3 a^{2} - a + 14\) , \( -a^{2} + a + 8\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-3a^{2}-a+14\right){x}-a^{2}+a+8$ |
| 31.1-b1 |
31.1-b |
$2$ |
$3$ |
3.3.1937.1 |
$3$ |
$[3, 0]$ |
31.1 |
\( 31 \) |
\( 31^{3} \) |
$6.97050$ |
$(-a^2-a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$148.2308786$ |
1.122671293 |
\( \frac{704728171}{29791} a^{2} - \frac{2306979864}{29791} a - \frac{308376675}{29791} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} - a - 5\) , \( a^{2} + 2 a + 1\) , \( 2 a^{2} + 4 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}+2a+1\right){x}+2a^{2}+4a-3$ |
*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.
