| 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 |
| 9216.2-a1 |
9216.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.431325727$ |
$3.226106002$ |
2.784522708 |
\( -\frac{6296000}{243} a - \frac{3592000}{243} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a + 7\) , \( a + 9\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-5a+7\right){x}+a+9$ |
| 9216.2-a2 |
9216.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{12} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.715662863$ |
$1.613053001$ |
2.784522708 |
\( \frac{31949000}{59049} a + \frac{40426000}{59049} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a + 17\) , \( -13 a + 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-5a+17\right){x}-13a+1$ |
| 9216.2-b1 |
9216.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.431325727$ |
$3.226106002$ |
2.784522708 |
\( \frac{6296000}{243} a - \frac{3296000}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 a + 2\) , \( -a + 10\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(5a+2\right){x}-a+10$ |
| 9216.2-b2 |
9216.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{12} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.715662863$ |
$1.613053001$ |
2.784522708 |
\( -\frac{31949000}{59049} a + \frac{24125000}{19683} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 a + 12\) , \( 13 a - 12\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(5a+12\right){x}+13a-12$ |
| 9216.2-c1 |
9216.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.345364298$ |
1.414307886 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( -8\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+8{x}-8$ |
| 9216.2-c2 |
9216.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.690728597$ |
1.414307886 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2{x}$ |
| 9216.2-c3 |
9216.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{2} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.345364298$ |
1.414307886 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -17\) , \( 33\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-17{x}+33$ |
| 9216.2-c4 |
9216.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{2} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.345364298$ |
1.414307886 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -32\) , \( -60\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-32{x}-60$ |
| 9216.2-d1 |
9216.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.181238623$ |
$2.294372107$ |
3.009050724 |
\( -\frac{664664}{729} a + \frac{35696}{243} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8\) , \( -8 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+8{x}-8a-8$ |
| 9216.2-d2 |
9216.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.362477247$ |
$4.588744215$ |
3.009050724 |
\( \frac{47168}{27} a - \frac{9152}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-2{x}$ |
| 9216.2-e1 |
9216.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{5} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.263572051$ |
1.523925232 |
\( \frac{579280888}{27} a - \frac{1719906040}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -95 a - 1\) , \( 533 a - 608\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-95a-1\right){x}+533a-608$ |
| 9216.2-e2 |
9216.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{11} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.263572051$ |
1.523925232 |
\( -\frac{1386944}{6561} a - \frac{29632}{2187} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5 a + 14\) , \( 32 a - 23\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a+14\right){x}+32a-23$ |
| 9216.2-e3 |
9216.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{14} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.263572051$ |
1.523925232 |
\( -\frac{1647302440}{531441} a + \frac{2224468216}{531441} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -15 a - 21\) , \( -27 a - 36\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a-21\right){x}-27a-36$ |
| 9216.2-e4 |
9216.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.527144102$ |
1.523925232 |
\( \frac{3348800}{729} a + \frac{570112}{729} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -5 a - 1\) , \( 11 a - 14\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-1\right){x}+11a-14$ |
| 9216.2-f1 |
9216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.006008013$ |
2.419336693 |
\( \frac{8069480}{81} a - \frac{19558064}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10 a - 21\) , \( 47 a + 21\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a-21\right){x}+47a+21$ |
| 9216.2-f2 |
9216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.006008013$ |
2.419336693 |
\( -\frac{248896}{9} a - 82176 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -15 a + 14\) , \( -8 a + 37\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a+14\right){x}-8a+37$ |
| 9216.2-f3 |
9216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.012016027$ |
2.419336693 |
\( -\frac{8000}{81} a + \frac{11456}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-{x}+a+1$ |
| 9216.2-f4 |
9216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{9} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.006008013$ |
2.419336693 |
\( \frac{6153304}{6561} a + \frac{11031680}{2187} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 1\) , \( -a + 25\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-1\right){x}-a+25$ |
| 9216.2-g1 |
9216.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.294372107$ |
1.383558438 |
\( \frac{664664}{729} a - \frac{557576}{729} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a + 7\) , \( -9 a + 9\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+7\right){x}-9a+9$ |
| 9216.2-g2 |
9216.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.588744215$ |
1.383558438 |
\( -\frac{47168}{27} a + \frac{19712}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a - 3\) , \( -a + 3\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-3\right){x}-a+3$ |
| 9216.2-h1 |
9216.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.608789983$ |
1.691113809 |
\( \frac{8000}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1\) , \( -a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+1\right){x}-a$ |
| 9216.2-h2 |
9216.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{4} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.804394991$ |
1.691113809 |
\( \frac{343000}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 11\) , \( 5 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+11\right){x}+5a-8$ |
| 9216.2-i1 |
9216.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.006008013$ |
1.209668346 |
\( -\frac{8069480}{81} a - \frac{3829528}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 12 a - 32\) , \( 36 a - 36\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(12a-32\right){x}+36a-36$ |
| 9216.2-i2 |
9216.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.006008013$ |
1.209668346 |
\( \frac{248896}{9} a - \frac{988480}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 17 a - 2\) , \( -24 a - 27\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a-2\right){x}-24a-27$ |
| 9216.2-i3 |
9216.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.012016027$ |
1.209668346 |
\( \frac{8000}{81} a + \frac{26368}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-2\right){x}$ |
| 9216.2-i4 |
9216.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{9} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.006008013$ |
1.209668346 |
\( -\frac{6153304}{6561} a + \frac{39248344}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8 a + 8\) , \( 8 a - 32\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a+8\right){x}+8a-32$ |
| 9216.2-j1 |
9216.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{5} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.263572051$ |
2.285887849 |
\( -\frac{579280888}{27} a - 42245376 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 97 a - 97\) , \( 437 a + 172\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(97a-97\right){x}+437a+172$ |
| 9216.2-j2 |
9216.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{11} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.263572051$ |
2.285887849 |
\( \frac{1386944}{6561} a - \frac{1475840}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a + 18\) , \( 36 a - 27\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+18\right){x}+36a-27$ |
| 9216.2-j3 |
9216.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{14} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.263572051$ |
2.285887849 |
\( \frac{1647302440}{531441} a + \frac{192388592}{177147} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 17 a - 37\) , \( -43 a + 100\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a-37\right){x}-43a+100$ |
| 9216.2-j4 |
9216.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.527144102$ |
2.285887849 |
\( -\frac{3348800}{729} a + \frac{1306304}{243} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 7 a - 7\) , \( 5 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a-7\right){x}+5a+10$ |
| 9216.2-k1 |
9216.2-k |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.294372107$ |
1.383558438 |
\( -\frac{664664}{729} a + \frac{35696}{243} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8\) , \( 8 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+8{x}+8a+8$ |
| 9216.2-k2 |
9216.2-k |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.588744215$ |
1.383558438 |
\( \frac{47168}{27} a - \frac{9152}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-2{x}$ |
| 9216.2-l1 |
9216.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.006008013$ |
1.209668346 |
\( \frac{8069480}{81} a - \frac{19558064}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -10 a - 21\) , \( -47 a - 21\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a-21\right){x}-47a-21$ |
| 9216.2-l2 |
9216.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.006008013$ |
1.209668346 |
\( -\frac{248896}{9} a - 82176 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15 a + 14\) , \( 8 a - 37\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-15a+14\right){x}+8a-37$ |
| 9216.2-l3 |
9216.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.012016027$ |
1.209668346 |
\( -\frac{8000}{81} a + \frac{11456}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1\) , \( -a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-{x}-a-1$ |
| 9216.2-l4 |
9216.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{9} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.006008013$ |
1.209668346 |
\( \frac{6153304}{6561} a + \frac{11031680}{2187} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 1\) , \( a - 25\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-1\right){x}+a-25$ |
| 9216.2-m1 |
9216.2-m |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{5} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.263572051$ |
2.285887849 |
\( \frac{579280888}{27} a - \frac{1719906040}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -95 a - 1\) , \( -533 a + 608\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-95a-1\right){x}-533a+608$ |
| 9216.2-m2 |
9216.2-m |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{11} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.263572051$ |
2.285887849 |
\( -\frac{1386944}{6561} a - \frac{29632}{2187} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a + 14\) , \( -32 a + 23\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a+14\right){x}-32a+23$ |
| 9216.2-m3 |
9216.2-m |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{14} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.263572051$ |
2.285887849 |
\( -\frac{1647302440}{531441} a + \frac{2224468216}{531441} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15 a - 21\) , \( 27 a + 36\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-15a-21\right){x}+27a+36$ |
| 9216.2-m4 |
9216.2-m |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.527144102$ |
2.285887849 |
\( \frac{3348800}{729} a + \frac{570112}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -5 a - 1\) , \( -11 a + 14\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a-1\right){x}-11a+14$ |
| 9216.2-n1 |
9216.2-n |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.181238623$ |
$2.294372107$ |
3.009050724 |
\( \frac{664664}{729} a - \frac{557576}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 7\) , \( 9 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+7\right){x}+9a-9$ |
| 9216.2-n2 |
9216.2-n |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.362477247$ |
$4.588744215$ |
3.009050724 |
\( -\frac{47168}{27} a + \frac{19712}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 3\) , \( a - 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-3\right){x}+a-3$ |
| 9216.2-o1 |
9216.2-o |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.608789983$ |
1.691113809 |
\( \frac{8000}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1\) , \( a\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}+a$ |
| 9216.2-o2 |
9216.2-o |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{4} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.804394991$ |
1.691113809 |
\( \frac{343000}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 11\) , \( -5 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+11\right){x}-5a+8$ |
| 9216.2-p1 |
9216.2-p |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{5} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.263572051$ |
1.523925232 |
\( -\frac{579280888}{27} a - 42245376 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 97 a - 97\) , \( -437 a - 172\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(97a-97\right){x}-437a-172$ |
| 9216.2-p2 |
9216.2-p |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{11} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.263572051$ |
1.523925232 |
\( \frac{1386944}{6561} a - \frac{1475840}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3 a + 18\) , \( -36 a + 27\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a+18\right){x}-36a+27$ |
| 9216.2-p3 |
9216.2-p |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{14} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.263572051$ |
1.523925232 |
\( \frac{1647302440}{531441} a + \frac{192388592}{177147} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 17 a - 37\) , \( 43 a - 100\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(17a-37\right){x}+43a-100$ |
| 9216.2-p4 |
9216.2-p |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.527144102$ |
1.523925232 |
\( -\frac{3348800}{729} a + \frac{1306304}{243} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 7 a - 7\) , \( -5 a - 10\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-7\right){x}-5a-10$ |
| 9216.2-q1 |
9216.2-q |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.006008013$ |
2.419336693 |
\( -\frac{8069480}{81} a - \frac{3829528}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 12 a - 32\) , \( -36 a + 36\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-32\right){x}-36a+36$ |
| 9216.2-q2 |
9216.2-q |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.90383$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.006008013$ |
2.419336693 |
\( \frac{248896}{9} a - \frac{988480}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 17 a - 2\) , \( 24 a + 27\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(17a-2\right){x}+24a+27$ |
*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.
