| 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 |
| 22275.9-a1 |
22275.9-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{9} \cdot 5^{6} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.214762679$ |
$1.096836904$ |
2.272764849 |
\( \frac{393194}{11} a - \frac{16965365}{11} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -33 a + 144\) , \( 319 a + 168\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-33a+144\right){x}+319a+168$ |
| 22275.9-a2 |
22275.9-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{9} \cdot 5^{6} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.429525359$ |
$2.193673808$ |
2.272764849 |
\( \frac{7136}{11} a + \frac{4759}{11} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a + 9\) , \( 7 a - 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-3a+9\right){x}+7a-3$ |
| 22275.9-b1 |
22275.9-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{9} \cdot 5^{6} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.595535165$ |
$1.096836904$ |
3.151179228 |
\( -\frac{393194}{11} a - 1506561 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -17 a - 126\) , \( 155 a + 561\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-17a-126\right){x}+155a+561$ |
| 22275.9-b2 |
22275.9-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{9} \cdot 5^{6} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.297767582$ |
$2.193673808$ |
3.151179228 |
\( -\frac{7136}{11} a + \frac{11895}{11} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -2 a - 6\) , \( 2 a + 12\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-2a-6\right){x}+2a+12$ |
| 22275.9-c1 |
22275.9-c |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{13} \cdot 5^{2} \cdot 11^{4} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$0.259779975$ |
$1.433897946$ |
3.593995674 |
\( \frac{94706}{363} a + \frac{524143}{363} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -a - 21\) , \( 3 a + 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-21\right){x}+3a+23$ |
| 22275.9-d1 |
22275.9-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{26} \cdot 5^{7} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.774289175$ |
$0.313585273$ |
5.368261923 |
\( \frac{772786757876}{263063295} a - \frac{611845250399}{263063295} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -144 a - 482\) , \( -2484 a - 2950\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-144a-482\right){x}-2484a-2950$ |
| 22275.9-d2 |
22275.9-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{19} \cdot 5^{8} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.887144587$ |
$0.627170546$ |
5.368261923 |
\( -\frac{2252642504}{601425} a + \frac{109962161}{601425} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 36 a - 167\) , \( -324 a + 830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(36a-167\right){x}-324a+830$ |
| 22275.9-e1 |
22275.9-e |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{15} \cdot 5^{10} \cdot 11^{3} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.257880721$ |
0.622031705 |
\( \frac{336572416}{121} a - \frac{914255872}{121} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -1077 a + 3084\) , \( 24459 a + 40781\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-1077a+3084\right){x}+24459a+40781$ |
| 22275.9-e2 |
22275.9-e |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{9} \cdot 5^{10} \cdot 11^{9} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.257880721$ |
0.622031705 |
\( -\frac{116936704}{161051} a + \frac{282554368}{161051} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -327 a - 291\) , \( -2441 a - 3169\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-327a-291\right){x}-2441a-3169$ |
| 22275.9-f1 |
22275.9-f |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{33} \cdot 5^{8} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$1.420521227$ |
$0.174707520$ |
3.591734471 |
\( -\frac{1765443371008}{473513931} a + \frac{1361708056576}{473513931} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -504 a - 1632\) , \( -10141 a - 26644\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-504a-1632\right){x}-10141a-26644$ |
| 22275.9-g1 |
22275.9-g |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{17} \cdot 5^{4} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.274248301$ |
$1.326591810$ |
5.265336769 |
\( \frac{1212416}{891} a - \frac{2588672}{891} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -18 a + 6\) , \( -33 a + 70\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-18a+6\right){x}-33a+70$ |
| 22275.9-h1 |
22275.9-h |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{15} \cdot 5^{8} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.371764661$ |
$0.897775172$ |
3.220248095 |
\( \frac{1823743}{2475} a - \frac{6007679}{825} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 4 a - 81\) , \( -24 a + 333\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a-81\right){x}-24a+333$ |
| 22275.9-h2 |
22275.9-h |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{24} \cdot 5^{7} \cdot 11^{8} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.974117292$ |
$0.112221896$ |
3.220248095 |
\( -\frac{824246964731}{480298005} a - \frac{2061152758066}{480298005} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2651 a + 3429\) , \( 15870 a - 153540\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2651a+3429\right){x}+15870a-153540$ |
| 22275.9-h3 |
22275.9-h |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{24} \cdot 5^{8} \cdot 11^{4} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1.487058646$ |
$0.224443793$ |
3.220248095 |
\( \frac{25678300333}{19847025} a - \frac{19537547749}{6615675} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 4 a + 1044\) , \( 9363 a - 7146\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a+1044\right){x}+9363a-7146$ |
| 22275.9-h4 |
22275.9-h |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{18} \cdot 5^{10} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.743529323$ |
$0.448887586$ |
3.220248095 |
\( -\frac{438412303}{556875} a - \frac{257207066}{185625} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 139 a - 126\) , \( 903 a + 549\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(139a-126\right){x}+903a+549$ |
| 22275.9-h5 |
22275.9-h |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{15} \cdot 5^{14} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.487058646$ |
$0.224443793$ |
3.220248095 |
\( \frac{153564491112713}{38671875} a + \frac{29579063849711}{12890625} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 2434 a - 2016\) , \( 53391 a + 21528\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(2434a-2016\right){x}+53391a+21528$ |
| 22275.9-h6 |
22275.9-h |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{30} \cdot 5^{7} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.974117292$ |
$0.112221896$ |
3.220248095 |
\( -\frac{18681448884772679}{2367569655} a + \frac{6520081742343122}{789189885} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 499 a + 17379\) , \( 542676 a - 339192\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(499a+17379\right){x}+542676a-339192$ |
| 22275.9-i1 |
22275.9-i |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{12} \cdot 5^{6} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cn, 5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$0.055202365$ |
1.664413941 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 211149 a - 70383\) , \( -28748141 a - 50309247\bigr] \) |
${y}^2+{y}={x}^{3}+\left(211149a-70383\right){x}-28748141a-50309247$ |
| 22275.9-i2 |
22275.9-i |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{12} \cdot 5^{6} \cdot 11^{10} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cn, 5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.276011827$ |
1.664413941 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 279 a - 93\) , \( -2501 a - 4377\bigr] \) |
${y}^2+{y}={x}^{3}+\left(279a-93\right){x}-2501a-4377$ |
| 22275.9-i3 |
22275.9-i |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{12} \cdot 5^{6} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cn, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.380059135$ |
1.664413941 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 9 a - 3\) , \( 19 a + 33\bigr] \) |
${y}^2+{y}={x}^{3}+\left(9a-3\right){x}+19a+33$ |
| 22275.9-j1 |
22275.9-j |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{13} \cdot 5^{9} \cdot 11^{6} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.277903186$ |
1.340655416 |
\( -\frac{303442335293}{13476375} a - \frac{724100828596}{4492125} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -715 a - 648\) , \( -13732 a + 1353\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-715a-648\right){x}-13732a+1353$ |
| 22275.9-j2 |
22275.9-j |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{27} \cdot 5^{7} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.277903186$ |
1.340655416 |
\( -\frac{90953656733}{29229255} a - \frac{48927807901}{9743085} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 510 a - 425\) , \( 5317 a + 2833\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(510a-425\right){x}+5317a+2833$ |
| 22275.9-j3 |
22275.9-j |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{21} \cdot 5^{8} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.555806373$ |
1.340655416 |
\( -\frac{15057467}{200475} a - \frac{65568874}{66825} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 15 a + 115\) , \( 511 a - 515\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(15a+115\right){x}+511a-515$ |
| 22275.9-j4 |
22275.9-j |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{11} \cdot 5^{12} \cdot 11^{3} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.555806373$ |
1.340655416 |
\( \frac{624671753}{17015625} a + \frac{3960100591}{5671875} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -70 a + 12\) , \( -115 a - 411\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-70a+12\right){x}-115a-411$ |
| 22275.9-k1 |
22275.9-k |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{17} \cdot 5^{10} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1.753273911$ |
$0.593269893$ |
5.017942960 |
\( \frac{1212416}{891} a - \frac{2588672}{891} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 18 a - 156\) , \( 83 a - 877\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(18a-156\right){x}+83a-877$ |
| 22275.9-l1 |
22275.9-l |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{33} \cdot 5^{2} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$3.881855343$ |
$0.390657891$ |
7.315762360 |
\( -\frac{1765443371008}{473513931} a + \frac{1361708056576}{473513931} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -216 a + 312\) , \( -285 a + 3319\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-216a+312\right){x}-285a+3319$ |
| 22275.9-m1 |
22275.9-m |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{15} \cdot 5^{4} \cdot 11^{3} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.576638824$ |
4.172715533 |
\( \frac{336572416}{121} a - \frac{914255872}{121} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 327 a + 141\) , \( -65 a - 5936\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(327a+141\right){x}-65a-5936$ |
| 22275.9-m2 |
22275.9-m |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{9} \cdot 5^{4} \cdot 11^{9} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.576638824$ |
4.172715533 |
\( -\frac{116936704}{161051} a + \frac{282554368}{161051} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -48 a + 141\) , \( 35 a + 514\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-48a+141\right){x}+35a+514$ |
| 22275.9-n1 |
22275.9-n |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{18} \cdot 5^{6} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.394023194$ |
$0.792309708$ |
5.328299371 |
\( \frac{19683}{11} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 45 a - 15\) , \( -32 a - 56\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(45a-15\right){x}-32a-56$ |
| 22275.9-n2 |
22275.9-n |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{18} \cdot 5^{6} \cdot 11^{4} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.788046389$ |
$0.396154854$ |
5.328299371 |
\( \frac{19034163}{121} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 450 a - 150\) , \( 2668 a + 4669\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(450a-150\right){x}+2668a+4669$ |
| 22275.9-o1 |
22275.9-o |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{17} \cdot 5^{10} \cdot 11^{8} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$11.67742443$ |
$0.056265412$ |
6.339313174 |
\( -\frac{4863869291539414}{247066875} a - \frac{4424195289931561}{27451875} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -365 a + 93721\) , \( 6663529 a - 3260012\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-365a+93721\right){x}+6663529a-3260012$ |
| 22275.9-o2 |
22275.9-o |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{37} \cdot 5^{8} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$5.838712218$ |
$0.112530824$ |
6.339313174 |
\( \frac{958122814426377008}{77668122532275} a - \frac{306009603519408749}{25889374177425} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 1570 a - 6674\) , \( 65125 a - 199094\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(1570a-6674\right){x}+65125a-199094$ |
| 22275.9-o3 |
22275.9-o |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{26} \cdot 5^{10} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$2.919356109$ |
$0.225061649$ |
6.339313174 |
\( \frac{260785336352}{3653656875} a - \frac{303574282031}{1217885625} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -275 a - 59\) , \( 6697 a - 7718\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-275a-59\right){x}+6697a-7718$ |
| 22275.9-o4 |
22275.9-o |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{23} \cdot 5^{22} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$2.919356109$ |
$0.056265412$ |
6.339313174 |
\( \frac{21019260087647753782}{11012420654296875} a + \frac{9080823717857207537}{11012420654296875} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 5485 a + 12271\) , \( -242495 a + 843196\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(5485a+12271\right){x}-242495a+843196$ |
| 22275.9-o5 |
22275.9-o |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{22} \cdot 5^{14} \cdot 11^{4} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$5.838712218$ |
$0.112530824$ |
6.339313174 |
\( -\frac{272628892055312}{34456640625} a + \frac{68270572626911}{11485546875} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 40 a + 5836\) , \( 104797 a - 46418\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(40a+5836\right){x}+104797a-46418$ |
| 22275.9-o6 |
22275.9-o |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{19} \cdot 5^{8} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.459678054$ |
$0.450123298$ |
6.339313174 |
\( -\frac{28291163072}{200475} a + \frac{39134601641}{66825} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -410 a - 14\) , \( 4285 a - 4064\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-410a-14\right){x}+4285a-4064$ |
| 22275.9-p1 |
22275.9-p |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{36} \cdot 5^{6} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{7} \) |
$1$ |
$0.152885330$ |
2.950186345 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -1175 a + 391\) , \( 4367 a + 7642\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-1175a+391\right){x}+4367a+7642$ |
| 22275.9-p2 |
22275.9-p |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{24} \cdot 5^{6} \cdot 11^{4} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.305770661$ |
2.950186345 |
\( \frac{169112377}{88209} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 310 a - 104\) , \( 407 a + 712\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(310a-104\right){x}+407a+712$ |
| 22275.9-p3 |
22275.9-p |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{42} \cdot 5^{6} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.076442665$ |
2.950186345 |
\( \frac{450360153235512010}{3106724901291} a + \frac{185226316549616531}{3106724901291} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -13280 a + 8176\) , \( -471445 a + 1225846\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-13280a+8176\right){x}-471445a+1225846$ |
| 22275.9-p4 |
22275.9-p |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{18} \cdot 5^{6} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.611541323$ |
2.950186345 |
\( \frac{30664297}{297} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 175 a - 59\) , \( -745 a - 1304\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(175a-59\right){x}-745a-1304$ |
| 22275.9-p5 |
22275.9-p |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{42} \cdot 5^{6} \cdot 11 \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.076442665$ |
2.950186345 |
\( -\frac{450360153235512010}{3106724901291} a + \frac{211862156595042847}{1035574967097} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -12830 a + 526\) , \( 709859 a - 808622\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-12830a+526\right){x}+709859a-808622$ |
| 22275.9-p6 |
22275.9-p |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{18} \cdot 5^{6} \cdot 11^{8} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.152885330$ |
2.950186345 |
\( \frac{347873904937}{395307} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 3955 a - 1319\) , \( 72335 a + 126586\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(3955a-1319\right){x}+72335a+126586$ |
| 22275.9-q1 |
22275.9-q |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{13} \cdot 5^{8} \cdot 11^{4} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.377315232$ |
$0.641258656$ |
7.003457045 |
\( \frac{94706}{363} a + \frac{524143}{363} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 67 a - 18\) , \( -173 a + 84\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(67a-18\right){x}-173a+84$ |
| 22275.9-r1 |
22275.9-r |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{6} \cdot 5^{6} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.376929126$ |
5.733368776 |
\( \frac{19683}{11} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 4 a - 2\) , \( -a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(4a-2\right){x}-a-2$ |
| 22275.9-r2 |
22275.9-r |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{6} \cdot 5^{6} \cdot 11^{4} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.188464563$ |
5.733368776 |
\( \frac{19034163}{121} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 49 a - 17\) , \( -121 a - 212\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(49a-17\right){x}-121a-212$ |
*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.
