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 |
5184.3-a1 |
5184.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{21} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.527579106$ |
$0.754285841$ |
1.919761085 |
\( -\frac{1688800}{729} a + \frac{3105712}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 57 a - 75\) , \( 220 a - 10\bigr] \) |
${y}^2={x}^{3}+\left(57a-75\right){x}+220a-10$ |
5184.3-a2 |
5184.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.263789553$ |
$1.508571683$ |
1.919761085 |
\( \frac{151552}{27} a + \frac{63488}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 30\) , \( -32 a + 53\bigr] \) |
${y}^2={x}^{3}+\left(12a-30\right){x}-32a+53$ |
5184.3-b1 |
5184.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{16} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.018351902$ |
1.228178605 |
\( \frac{868}{27} a - \frac{856}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 a - 3\) , \( -72 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(9a-3\right){x}-72a-2$ |
5184.3-b2 |
5184.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{20} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.509175951$ |
1.228178605 |
\( \frac{18321686}{729} a - \frac{567362}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 a + 357\) , \( -1584 a + 1006\bigr] \) |
${y}^2={x}^{3}+\left(9a+357\right){x}-1584a+1006$ |
5184.3-c1 |
5184.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{21} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.527579106$ |
$0.754285841$ |
1.919761085 |
\( \frac{1688800}{729} a + \frac{472304}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -57 a - 18\) , \( -220 a + 210\bigr] \) |
${y}^2={x}^{3}+\left(-57a-18\right){x}-220a+210$ |
5184.3-c2 |
5184.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.263789553$ |
$1.508571683$ |
1.919761085 |
\( -\frac{151552}{27} a + \frac{71680}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a - 18\) , \( 32 a + 21\bigr] \) |
${y}^2={x}^{3}+\left(-12a-18\right){x}+32a+21$ |
5184.3-d1 |
5184.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{12} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.408164878$ |
1.698310743 |
\( 2916 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 a - 27\) , \( -16 a + 30\bigr] \) |
${y}^2={x}^{3}+\left(9a-27\right){x}-16a+30$ |
5184.3-d2 |
5184.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{12} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.704082439$ |
1.698310743 |
\( 4293378 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 129 a - 387\) , \( -1360 a + 2550\bigr] \) |
${y}^2={x}^{3}+\left(129a-387\right){x}-1360a+2550$ |
5184.3-e1 |
5184.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{16} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.018351902$ |
1.228178605 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a + 6\) , \( 72 a - 74\bigr] \) |
${y}^2={x}^{3}+\left(-9a+6\right){x}+72a-74$ |
5184.3-e2 |
5184.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{20} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.509175951$ |
1.228178605 |
\( -\frac{18321686}{729} a + \frac{5918108}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a + 366\) , \( 1584 a - 578\bigr] \) |
${y}^2={x}^{3}+\left(-9a+366\right){x}+1584a-578$ |
5184.3-f1 |
5184.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{14} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.604802859$ |
$1.509372256$ |
4.403863396 |
\( \frac{74896}{243} a + \frac{333536}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 3\) , \( 12 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(12a-3\right){x}+12a-2$ |
5184.3-f2 |
5184.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{19} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.209605719$ |
$0.754686128$ |
4.403863396 |
\( -\frac{20798116}{59049} a + \frac{115993444}{59049} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -48 a - 3\) , \( 96 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-48a-3\right){x}+96a-2$ |
5184.3-g1 |
5184.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{11} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.101491900$ |
2.656898432 |
\( -\frac{901156}{9} a - \frac{2237696}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -63 a - 3\) , \( -256 a + 262\bigr] \) |
${y}^2={x}^{3}+\left(-63a-3\right){x}-256a+262$ |
5184.3-g2 |
5184.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{10} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.202983801$ |
2.656898432 |
\( \frac{496}{3} a + \frac{1136}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a - 3\) , \( -4 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(-3a-3\right){x}-4a+10$ |
5184.3-h1 |
5184.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{12} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.408164878$ |
1.698310743 |
\( 2916 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a - 18\) , \( 16 a + 14\bigr] \) |
${y}^2={x}^{3}+\left(-9a-18\right){x}+16a+14$ |
5184.3-h2 |
5184.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{12} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.704082439$ |
1.698310743 |
\( 4293378 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -129 a - 258\) , \( 1360 a + 1190\bigr] \) |
${y}^2={x}^{3}+\left(-129a-258\right){x}+1360a+1190$ |
5184.3-i1 |
5184.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{14} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.604802859$ |
$1.509372256$ |
4.403863396 |
\( -\frac{74896}{243} a + \frac{136144}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 9\) , \( -12 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(-12a+9\right){x}-12a+10$ |
5184.3-i2 |
5184.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{19} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.209605719$ |
$0.754686128$ |
4.403863396 |
\( \frac{20798116}{59049} a + \frac{31731776}{19683} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 48 a - 51\) , \( -96 a + 94\bigr] \) |
${y}^2={x}^{3}+\left(48a-51\right){x}-96a+94$ |
5184.3-j1 |
5184.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{11} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.101491900$ |
2.656898432 |
\( \frac{901156}{9} a - \frac{1046284}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 63 a - 66\) , \( 256 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(63a-66\right){x}+256a+6$ |
5184.3-j2 |
5184.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{10} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.202983801$ |
2.656898432 |
\( -\frac{496}{3} a + 544 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a - 6\) , \( 4 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(3a-6\right){x}+4a+6$ |
5184.3-k1 |
5184.3-k |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{28} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.302945584$ |
2.922928979 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 141\) , \( 4718\bigr] \) |
${y}^2={x}^{3}+141{x}+4718$ |
5184.3-k2 |
5184.3-k |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{14} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.423564678$ |
2.922928979 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -7\bigr] \) |
${y}^2={x}^{3}+6{x}-7$ |
5184.3-k3 |
5184.3-k |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{16} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.211782339$ |
2.922928979 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \) |
${y}^2={x}^{3}-39{x}-70$ |
5184.3-k4 |
5184.3-k |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{20} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.605891169$ |
2.922928979 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -219\) , \( 1190\bigr] \) |
${y}^2={x}^{3}-219{x}+1190$ |
5184.3-k5 |
5184.3-k |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{14} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.605891169$ |
2.922928979 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -579\) , \( -5362\bigr] \) |
${y}^2={x}^{3}-579{x}-5362$ |
5184.3-k6 |
5184.3-k |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{16} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.302945584$ |
2.922928979 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3459\) , \( 78302\bigr] \) |
${y}^2={x}^{3}-3459{x}+78302$ |
*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.