| 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 |
$4$ |
$4$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{16} \) |
$4.36592$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$12.05557311$ |
1.290640067 |
\( \frac{2400694423446565892}{152587890625} a^{2} - \frac{8490114795873851837}{152587890625} a + \frac{4752340914414381276}{152587890625} \) |
\( \bigl[a^{2} + a - 5\) , \( 0\) , \( a^{2} - 5\) , \( -5203 a^{2} + 18404 a - 10262\) , \( -602834 a^{2} + 2131983 a - 1188249\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-5203a^{2}+18404a-10262\right){x}-602834a^{2}+2131983a-1188249$ |
| 5.1-a2 |
5.1-a |
$4$ |
$4$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$4.36592$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$48.22229246$ |
1.290640067 |
\( -\frac{28451318558610513919684}{625} a^{2} + \frac{8728149441979146219949}{625} a + \frac{205209802475645542893748}{625} \) |
\( \bigl[a^{2} + a - 5\) , \( 0\) , \( a^{2} - 5\) , \( -973 a^{2} + 3454 a - 1932\) , \( 37404 a^{2} - 132263 a + 73709\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-973a^{2}+3454a-1932\right){x}+37404a^{2}-132263a+73709$ |
| 5.1-a3 |
5.1-a |
$4$ |
$4$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$4.36592$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$96.44458492$ |
1.290640067 |
\( -\frac{1000097191662047}{390625} a^{2} + \frac{306803558641792}{390625} a + \frac{7213368964309384}{390625} \) |
\( \bigl[a^{2} + a - 5\) , \( 0\) , \( a^{2} - 5\) , \( -328 a^{2} + 1169 a - 657\) , \( -9155 a^{2} + 32388 a - 18056\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-328a^{2}+1169a-657\right){x}-9155a^{2}+32388a-18056$ |
| 5.1-a4 |
5.1-a |
$4$ |
$4$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$4.36592$ |
$(-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$192.8891698$ |
1.290640067 |
\( \frac{45962184}{625} a^{2} + \frac{59059426}{625} a - \frac{145904373}{625} \) |
\( \bigl[a^{2} + a - 5\) , \( 0\) , \( a^{2} - 5\) , \( 17 a^{2} - 51 a + 23\) , \( -580 a^{2} + 2062 a - 1154\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(17a^{2}-51a+23\right){x}-580a^{2}+2062a-1154$ |
| 5.1-b1 |
5.1-b |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$4.36592$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$88.82987098$ |
2.377476989 |
\( \frac{38440684463}{625} a^{2} - \frac{149920969943}{625} a + \frac{115496111289}{625} \) |
\( \bigl[a\) , \( a^{2} + a - 6\) , \( 1\) , \( -21 a^{2} + 93 a - 80\) , \( 222 a^{2} - 768 a + 401\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-21a^{2}+93a-80\right){x}+222a^{2}-768a+401$ |
| 5.1-b2 |
5.1-b |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$4.36592$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$177.6597419$ |
2.377476989 |
\( \frac{289149}{25} a^{2} + \frac{746086}{25} a - \frac{811578}{25} \) |
\( \bigl[a\) , \( a^{2} + a - 6\) , \( 1\) , \( -a^{2} + 8 a\) , \( 5 a^{2} - 11 a + 3\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-a^{2}+8a\right){x}+5a^{2}-11a+3$ |
| 5.1-c1 |
5.1-c |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$4.36592$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.983978448$ |
$75.19125212$ |
2.970307785 |
\( \frac{38440684463}{625} a^{2} - \frac{149920969943}{625} a + \frac{115496111289}{625} \) |
\( \bigl[1\) , \( a^{2} + a - 6\) , \( a\) , \( -11 a^{2} + 38 a - 15\) , \( -49 a^{2} + 173 a - 99\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-11a^{2}+38a-15\right){x}-49a^{2}+173a-99$ |
| 5.1-c2 |
5.1-c |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$4.36592$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.491989224$ |
$150.3825042$ |
2.970307785 |
\( \frac{289149}{25} a^{2} + \frac{746086}{25} a - \frac{811578}{25} \) |
\( \bigl[1\) , \( a^{2} + a - 6\) , \( a\) , \( -a^{2} + 3 a + 5\) , \( 2 a - 5\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-a^{2}+3a+5\right){x}+2a-5$ |
| 5.1-d1 |
5.1-d |
$4$ |
$4$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{16} \) |
$4.36592$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.921833868$ |
$19.84650192$ |
0.734488804 |
\( \frac{2400694423446565892}{152587890625} a^{2} - \frac{8490114795873851837}{152587890625} a + \frac{4752340914414381276}{152587890625} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( 1\) , \( -12754 a^{2} + 45104 a - 25134\) , \( 2292968 a^{2} - 8109378 a + 4519712\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-12754a^{2}+45104a-25134\right){x}+2292968a^{2}-8109378a+4519712$ |
| 5.1-d2 |
5.1-d |
$4$ |
$4$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$4.36592$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.687335472$ |
$4.961625482$ |
0.734488804 |
\( -\frac{28451318558610513919684}{625} a^{2} + \frac{8728149441979146219949}{625} a + \frac{205209802475645542893748}{625} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( 1\) , \( -2384 a^{2} + 8454 a - 4764\) , \( -147228 a^{2} + 520726 a - 290304\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-2384a^{2}+8454a-4764\right){x}-147228a^{2}+520726a-290304$ |
| 5.1-d3 |
5.1-d |
$4$ |
$4$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$4.36592$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.843667736$ |
$39.69300385$ |
0.734488804 |
\( -\frac{1000097191662047}{390625} a^{2} + \frac{306803558641792}{390625} a + \frac{7213368964309384}{390625} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( 1\) , \( -809 a^{2} + 2859 a - 1589\) , \( 33868 a^{2} - 119778 a + 66756\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-809a^{2}+2859a-1589\right){x}+33868a^{2}-119778a+66756$ |
| 5.1-d4 |
5.1-d |
$4$ |
$4$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$4.36592$ |
$(-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.921833868$ |
$79.38600771$ |
0.734488804 |
\( \frac{45962184}{625} a^{2} + \frac{59059426}{625} a - \frac{145904373}{625} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( 1\) , \( 36 a^{2} - 131 a + 81\) , \( 2292 a^{2} - 8104 a + 4512\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(36a^{2}-131a+81\right){x}+2292a^{2}-8104a+4512$ |
| 10.1-a1 |
10.1-a |
$1$ |
$1$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{2} \) |
$4.90059$ |
$(-a+3), (a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$24.29552432$ |
1.300509600 |
\( -\frac{902609}{200} a^{2} - \frac{883201}{100} a + \frac{327961}{40} \) |
\( \bigl[a^{2} + a - 5\) , \( 1\) , \( a^{2} + a - 4\) , \( 26 a^{2} - 6 a - 182\) , \( 613 a^{2} - 184 a - 4411\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+{x}^{2}+\left(26a^{2}-6a-182\right){x}+613a^{2}-184a-4411$ |
| 10.1-b1 |
10.1-b |
$2$ |
$3$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{15} \cdot 5^{6} \) |
$4.90059$ |
$(-a+3), (a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$12.00741419$ |
1.928226437 |
\( \frac{112128657050479}{500000} a^{2} - \frac{34445868993263}{500000} a - \frac{161773421560101}{100000} \) |
\( \bigl[a^{2} + a - 5\) , \( 1\) , \( a^{2} - 5\) , \( 11 a^{2} - 2 a - 63\) , \( -18 a^{2} + 38 a + 60\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+{x}^{2}+\left(11a^{2}-2a-63\right){x}-18a^{2}+38a+60$ |
| 10.1-b2 |
10.1-b |
$2$ |
$3$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5^{2} \) |
$4.90059$ |
$(-a+3), (a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$36.02224259$ |
1.928226437 |
\( -\frac{9930181}{50} a^{2} + \frac{70278239}{100} a - \frac{7846297}{20} \) |
\( \bigl[a^{2} + a - 5\) , \( 1\) , \( a^{2} - 5\) , \( a^{2} + 8 a - 8\) , \( 16 a - 13\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+{x}^{2}+\left(a^{2}+8a-8\right){x}+16a-13$ |
| 10.1-c1 |
10.1-c |
$2$ |
$3$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5^{2} \) |
$4.90059$ |
$(-a+3), (a^2-6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1.727892073$ |
$76.86389658$ |
2.369763691 |
\( -\frac{9930181}{50} a^{2} + \frac{70278239}{100} a - \frac{7846297}{20} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 6\) , \( 0\) , \( a^{2} + 5 a - 2\) , \( a^{2} - 1\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(a^{2}+5a-2\right){x}+a^{2}-1$ |
| 10.1-c2 |
10.1-c |
$2$ |
$3$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{15} \cdot 5^{6} \) |
$4.90059$ |
$(-a+3), (a^2-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$5.183676219$ |
$2.846810984$ |
2.369763691 |
\( \frac{112128657050479}{500000} a^{2} - \frac{34445868993263}{500000} a - \frac{161773421560101}{100000} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 6\) , \( 0\) , \( -29 a^{2} - 55 a + 53\) , \( -279 a^{2} - 528 a + 500\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-29a^{2}-55a+53\right){x}-279a^{2}-528a+500$ |
| 10.1-d1 |
10.1-d |
$1$ |
$1$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{2} \) |
$4.90059$ |
$(-a+3), (a^2-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.132315019$ |
$52.88248349$ |
1.123646046 |
\( -\frac{902609}{200} a^{2} - \frac{883201}{100} a + \frac{327961}{40} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 6\) , \( a^{2} + a - 4\) , \( -2 a^{2} - 6 a - 1\) , \( -14 a^{2} - 23 a + 32\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-2a^{2}-6a-1\right){x}-14a^{2}-23a+32$ |
| 10.2-a1 |
10.2-a |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$4.90059$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$132.5634432$ |
3.547979215 |
\( -\frac{5055411487375307}{10} a^{2} + \frac{775436591104079}{5} a + \frac{7292596936246757}{2} \) |
\( \bigl[a\) , \( a\) , \( a^{2} - 4\) , \( -5 a^{2} + 14 a - 8\) , \( -14 a^{2} + 48 a - 29\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(-5a^{2}+14a-8\right){x}-14a^{2}+48a-29$ |
| 10.2-a2 |
10.2-a |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$4.90059$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$132.5634432$ |
3.547979215 |
\( \frac{426636057}{50} a^{2} - \frac{130789183}{50} a - \frac{307694898}{5} \) |
\( \bigl[a\) , \( a\) , \( a^{2} - 4\) , \( -a + 2\) , \( -a^{2} + 2 a - 4\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(-a+2\right){x}-a^{2}+2a-4$ |
| 10.2-b1 |
10.2-b |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5^{10} \) |
$4.90059$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$75.24422017$ |
4.027730762 |
\( \frac{63521587627689}{39062500} a^{2} - \frac{5442805749933}{19531250} a - \frac{87257374729027}{7812500} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 5\) , \( a^{2} - 5\) , \( -4 a^{2} - 14 a + 3\) , \( 9 a^{2} + 14 a - 18\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-4a^{2}-14a+3\right){x}+9a^{2}+14a-18$ |
| 10.2-b2 |
10.2-b |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{5} \) |
$4.90059$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$75.24422017$ |
4.027730762 |
\( -\frac{50002885222410754}{3125} a^{2} + \frac{32311366451276077}{6250} a + \frac{145089616528311519}{1250} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 5\) , \( a^{2} - 5\) , \( -109 a^{2} - 194 a + 158\) , \( 1254 a^{2} + 2360 a - 2195\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-109a^{2}-194a+158\right){x}+1254a^{2}+2360a-2195$ |
| 10.2-c1 |
10.2-c |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{5} \) |
$4.90059$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$16.46359734$ |
0.881276160 |
\( -\frac{50002885222410754}{3125} a^{2} + \frac{32311366451276077}{6250} a + \frac{145089616528311519}{1250} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} - 4\) , \( a^{2} + a - 5\) , \( 172 a^{2} - 24 a - 1294\) , \( 2383 a^{2} - 746 a - 17104\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(172a^{2}-24a-1294\right){x}+2383a^{2}-746a-17104$ |
| 10.2-c2 |
10.2-c |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5^{10} \) |
$4.90059$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.46359734$ |
0.881276160 |
\( \frac{63521587627689}{39062500} a^{2} - \frac{5442805749933}{19531250} a - \frac{87257374729027}{7812500} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} - 4\) , \( a^{2} + a - 5\) , \( 17 a^{2} - 4 a - 89\) , \( 47 a^{2} - 12 a - 278\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(17a^{2}-4a-89\right){x}+47a^{2}-12a-278$ |
| 10.2-d1 |
10.2-d |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$4.90059$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$38.65677423$ |
1.034624841 |
\( -\frac{5055411487375307}{10} a^{2} + \frac{775436591104079}{5} a + \frac{7292596936246757}{2} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 6\) , \( a^{2} + a - 4\) , \( 6 a^{2} + 31 a - 147\) , \( 97 a^{2} - 167 a - 320\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(6a^{2}+31a-147\right){x}+97a^{2}-167a-320$ |
| 10.2-d2 |
10.2-d |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$4.90059$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$38.65677423$ |
1.034624841 |
\( \frac{426636057}{50} a^{2} - \frac{130789183}{50} a - \frac{307694898}{5} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 6\) , \( a^{2} + a - 4\) , \( a^{2} - 4 a - 7\) , \( 3 a^{2} - 14 a + 5\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(a^{2}-4a-7\right){x}+3a^{2}-14a+5$ |
| 10.3-a1 |
10.3-a |
$1$ |
$1$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{8} \) |
$4.90059$ |
$(-a+3), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$22.04642691$ |
3.540354529 |
\( -\frac{768520493}{781250} a^{2} - \frac{1454212727}{781250} a + \frac{457945371}{781250} \) |
\( \bigl[1\) , \( a^{2} + a - 6\) , \( a + 1\) , \( -97 a^{2} - 179 a + 172\) , \( -1512 a^{2} - 2788 a + 2656\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-97a^{2}-179a+172\right){x}-1512a^{2}-2788a+2656$ |
| 10.3-b1 |
10.3-b |
$1$ |
$1$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{8} \) |
$4.90059$ |
$(-a+3), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.095424557$ |
$22.32850648$ |
4.105911795 |
\( -\frac{768520493}{781250} a^{2} - \frac{1454212727}{781250} a + \frac{457945371}{781250} \) |
\( \bigl[a\) , \( a^{2} + a - 6\) , \( a^{2} + a - 4\) , \( 38 a^{2} - 12 a - 275\) , \( -457 a^{2} + 135 a + 3283\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(38a^{2}-12a-275\right){x}-457a^{2}+135a+3283$ |
| 11.1-a1 |
11.1-a |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$4.97905$ |
$(-a^2+2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$357.4921120$ |
2.392014253 |
\( \frac{12288}{11} a^{2} - \frac{28672}{11} a + \frac{12288}{11} \) |
\( \bigl[0\) , \( -a^{2} + 6\) , \( 1\) , \( -2 a^{2} + 3 a + 9\) , \( -3 a + 8\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-2a^{2}+3a+9\right){x}-3a+8$ |
| 11.1-a2 |
11.1-a |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$4.97905$ |
$(-a^2+2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$178.7460560$ |
2.392014253 |
\( -\frac{7061504}{121} a^{2} + \frac{2085088}{121} a + \frac{51290768}{121} \) |
\( \bigl[a + 1\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( 751261 a^{2} + 1384881 a - 1321049\) , \( -680956504 a^{2} - 1255278274 a + 1197431649\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(751261a^{2}+1384881a-1321049\right){x}-680956504a^{2}-1255278274a+1197431649$ |
| 11.1-b1 |
11.1-b |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$4.97905$ |
$(-a^2+2a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.117915434$ |
$114.3151844$ |
5.130520457 |
\( -\frac{7061504}{121} a^{2} + \frac{2085088}{121} a + \frac{51290768}{121} \) |
\( \bigl[a^{2} + a - 4\) , \( -a + 1\) , \( 1\) , \( 104105778 a^{2} + 191909058 a - 183065365\) , \( -1110715033559 a^{2} - 2047497077012 a + 1953142858336\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(104105778a^{2}+191909058a-183065365\right){x}-1110715033559a^{2}-2047497077012a+1953142858336$ |
| 11.1-b2 |
11.1-b |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$4.97905$ |
$(-a^2+2a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.235830869$ |
$114.3151844$ |
5.130520457 |
\( \frac{12288}{11} a^{2} - \frac{28672}{11} a + \frac{12288}{11} \) |
\( \bigl[0\) , \( a^{2} - a - 6\) , \( a\) , \( -3 a^{2} - a + 15\) , \( -9\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-3a^{2}-a+15\right){x}-9$ |
| 20.3-a1 |
20.3-a |
$4$ |
$6$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$49.45815632$ |
1.985575808 |
\( \frac{18144}{25} a^{2} + \frac{72864}{25} a - \frac{6592}{5} \) |
\( \bigl[a^{2} - 5\) , \( a - 1\) , \( 0\) , \( -3 a^{2} - 4 a + 12\) , \( -9 a^{2} - 15 a + 19\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a^{2}-4a+12\right){x}-9a^{2}-15a+19$ |
| 20.3-a2 |
20.3-a |
$4$ |
$6$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$16.48605210$ |
1.985575808 |
\( \frac{2378736270617184}{15625} a^{2} + \frac{4384972713907104}{15625} a - \frac{836580531349312}{3125} \) |
\( \bigl[a^{2} - 5\) , \( a - 1\) , \( 0\) , \( -203 a^{2} - 374 a + 362\) , \( -4073 a^{2} - 7507 a + 7163\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-203a^{2}-374a+362\right){x}-4073a^{2}-7507a+7163$ |
| 20.3-a3 |
20.3-a |
$4$ |
$6$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( - 2^{4} \cdot 5^{4} \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$49.45815632$ |
1.985575808 |
\( \frac{809637436}{625} a^{2} - \frac{2864159384}{625} a + \frac{319628652}{125} \) |
\( \bigl[a + 1\) , \( a^{2} - 6\) , \( a^{2} - 5\) , \( 4209 a^{2} + 7762 a - 7392\) , \( -1506114 a^{2} - 2776380 a + 2648427\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(4209a^{2}+7762a-7392\right){x}-1506114a^{2}-2776380a+2648427$ |
| 20.3-a4 |
20.3-a |
$4$ |
$6$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( - 2^{4} \cdot 5^{12} \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$16.48605210$ |
1.985575808 |
\( -\frac{238031359060300644}{244140625} a^{2} + \frac{72961758716982136}{244140625} a + \frac{343337563102814092}{48828125} \) |
\( \bigl[a + 1\) , \( a^{2} - 6\) , \( a^{2} - 5\) , \( -337566 a^{2} - 622268 a + 593603\) , \( -257569576 a^{2} - 474804914 a + 452924609\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-337566a^{2}-622268a+593603\right){x}-257569576a^{2}-474804914a+452924609$ |
| 20.3-b1 |
20.3-b |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$293.6828157$ |
1.965060088 |
\( \frac{171968}{5} a^{2} - \frac{616192}{5} a + 74304 \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 6\) , \( a^{2} + a - 4\) , \( -26804477987 a^{2} - 49411495005 a + 47134479291\) , \( 1968555136891523 a^{2} + 3628843372909587 a - 3461616427878475\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-26804477987a^{2}-49411495005a+47134479291\right){x}+1968555136891523a^{2}+3628843372909587a-3461616427878475$ |
| 20.3-b2 |
20.3-b |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$146.8414078$ |
1.965060088 |
\( \frac{2130144}{25} a^{2} + \frac{3932064}{25} a - \frac{747712}{5} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 5\) , \( a^{2} - 5\) , \( -3 a^{2} + 19\) , \( -3 a^{2} + 2 a + 24\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-3a^{2}+19\right){x}-3a^{2}+2a+24$ |
| 20.3-c1 |
20.3-c |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$93.02599443$ |
1.244891829 |
\( \frac{2130144}{25} a^{2} + \frac{3932064}{25} a - \frac{747712}{5} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 6\) , \( 0\) , \( -9 a^{2} + 4 a + 68\) , \( -50 a^{2} + 16 a + 362\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-9a^{2}+4a+68\right){x}-50a^{2}+16a+362$ |
| 20.3-c2 |
20.3-c |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$186.0519888$ |
1.244891829 |
\( \frac{171968}{5} a^{2} - \frac{616192}{5} a + 74304 \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 6\) , \( a^{2} + a - 4\) , \( -193430392 a^{2} - 356570442 a + 340138748\) , \( 1206574057641 a^{2} + 2224204032172 a - 2121706677669\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-193430392a^{2}-356570442a+340138748\right){x}+1206574057641a^{2}+2224204032172a-2121706677669$ |
| 20.3-d1 |
20.3-d |
$4$ |
$6$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$4.110077794$ |
0.495016695 |
\( \frac{2378736270617184}{15625} a^{2} + \frac{4384972713907104}{15625} a - \frac{836580531349312}{3125} \) |
\( \bigl[a^{2} - 5\) , \( 0\) , \( a^{2} - 5\) , \( 19 a^{2} - 10 a - 145\) , \( 125 a^{2} - 46 a - 922\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(19a^{2}-10a-145\right){x}+125a^{2}-46a-922$ |
| 20.3-d2 |
20.3-d |
$4$ |
$6$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$110.9721004$ |
0.495016695 |
\( \frac{18144}{25} a^{2} + \frac{72864}{25} a - \frac{6592}{5} \) |
\( \bigl[a^{2} - 5\) , \( 0\) , \( a^{2} - 5\) , \( -a^{2} + 5\) , \( -a^{2} + 6\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+5\right){x}-a^{2}+6$ |
| 20.3-d3 |
20.3-d |
$4$ |
$6$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( - 2^{4} \cdot 5^{4} \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$110.9721004$ |
0.495016695 |
\( \frac{809637436}{625} a^{2} - \frac{2864159384}{625} a + \frac{319628652}{125} \) |
\( \bigl[a^{2} + a - 4\) , \( 1\) , \( a^{2} - 5\) , \( 35 a^{2} + 63 a - 65\) , \( -789 a^{2} - 1456 a + 1383\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+{x}^{2}+\left(35a^{2}+63a-65\right){x}-789a^{2}-1456a+1383$ |
| 20.3-d4 |
20.3-d |
$4$ |
$6$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
20.3 |
\( 2^{2} \cdot 5 \) |
\( - 2^{4} \cdot 5^{12} \) |
$5.50072$ |
$(-a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$4.110077794$ |
0.495016695 |
\( -\frac{238031359060300644}{244140625} a^{2} + \frac{72961758716982136}{244140625} a + \frac{343337563102814092}{48828125} \) |
\( \bigl[a^{2} + a - 4\) , \( 1\) , \( a^{2} - 5\) , \( -2420 a^{2} - 4487 a + 4190\) , \( -167995 a^{2} - 309794 a + 295129\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+{x}^{2}+\left(-2420a^{2}-4487a+4190\right){x}-167995a^{2}-309794a+295129$ |
| 22.1-a1 |
22.1-a |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{4} \cdot 11^{2} \) |
$5.58880$ |
$(-a+3), (-a^2+2a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.940259949$ |
$38.49564142$ |
2.906283951 |
\( \frac{2053105}{484} a^{2} + \frac{7369277}{242} a - \frac{11895071}{484} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} + a - 6\) , \( a^{2} + a - 5\) , \( -2 a^{2} - 6 a - 2\) , \( -a - 3\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-2a^{2}-6a-2\right){x}-a-3$ |
| 22.1-a2 |
22.1-a |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{2} \cdot 11^{4} \) |
$5.58880$ |
$(-a+3), (-a^2+2a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.880519899$ |
$19.24782071$ |
2.906283951 |
\( \frac{4764146898377}{14641} a^{2} - \frac{33757096553365}{29282} a + \frac{18949366665621}{29282} \) |
\( \bigl[a^{2} + a - 5\) , \( a^{2} + a - 6\) , \( a^{2} + a - 5\) , \( -7 a^{2} - 16 a + 3\) , \( -68 a^{2} - 127 a + 115\bigr] \) |
${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-7a^{2}-16a+3\right){x}-68a^{2}-127a+115$ |
| 22.1-b1 |
22.1-b |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{2} \cdot 11^{4} \) |
$5.58880$ |
$(-a+3), (-a^2+2a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.036291425$ |
$167.3351089$ |
2.925640032 |
\( \frac{4764146898377}{14641} a^{2} - \frac{33757096553365}{29282} a + \frac{18949366665621}{29282} \) |
\( \bigl[1\) , \( -a^{2} + 6\) , \( a^{2} - 5\) , \( 35 a^{2} - 10 a - 256\) , \( -160 a^{2} + 48 a + 1155\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(35a^{2}-10a-256\right){x}-160a^{2}+48a+1155$ |
| 22.1-b2 |
22.1-b |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{4} \cdot 11^{2} \) |
$5.58880$ |
$(-a+3), (-a^2+2a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.036291425$ |
$334.6702179$ |
2.925640032 |
\( \frac{2053105}{484} a^{2} + \frac{7369277}{242} a - \frac{11895071}{484} \) |
\( \bigl[1\) , \( -a^{2} + 6\) , \( a^{2} - 5\) , \( -1\) , \( -a^{2} + 6\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}-{x}-a^{2}+6$ |
| 25.1-a1 |
25.1-a |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{7} \) |
$5.70915$ |
$(-a), (a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$42.83215803$ |
1.719564640 |
\( -\frac{600358912}{15625} a^{2} - \frac{845275136}{15625} a + \frac{347107328}{3125} \) |
\( \bigl[0\) , \( a^{2} - 6\) , \( a^{2} - 4\) , \( -32 a^{2} - 56 a + 64\) , \( -244 a^{2} - 452 a + 422\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-32a^{2}-56a+64\right){x}-244a^{2}-452a+422$ |
| 25.1-a2 |
25.1-a |
$2$ |
$2$ |
3.3.1396.1 |
$3$ |
$[3, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{5} \) |
$5.70915$ |
$(-a), (a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$42.83215803$ |
1.719564640 |
\( \frac{1355176800416}{125} a^{2} + \frac{2498138890208}{125} a - \frac{476603580368}{25} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 5\) , \( a^{2} - 4\) , \( -15707886356 a^{2} - 28955988193 a + 27621617731\) , \( -2577226701265225 a^{2} - 4750871265988477 a + 4531938232400326\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-15707886356a^{2}-28955988193a+27621617731\right){x}-2577226701265225a^{2}-4750871265988477a+4531938232400326$ |
*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.
