| 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 |
| 14400.9-a1 |
14400.9-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{7} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.121903780$ |
$1.657820380$ |
3.899763591 |
\( -\frac{256}{45} a - \frac{512}{15} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a + 3\) , \( 2 a - 32\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+3\right){x}+2a-32$ |
| 14400.9-a2 |
14400.9-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{7} \cdot 5^{8} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.121903780$ |
$0.828910190$ |
3.899763591 |
\( -\frac{1192336}{75} a + \frac{625008}{25} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 52 a + 68\) , \( 132 a - 492\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(52a+68\right){x}+132a-492$ |
| 14400.9-b1 |
14400.9-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{10} \cdot 5^{9} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.519407649$ |
$0.889374621$ |
2.228520910 |
\( \frac{1035520}{81} a - \frac{469504}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -48 a + 93\) , \( 52 a + 343\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-48a+93\right){x}+52a+343$ |
| 14400.9-b2 |
14400.9-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{14} \cdot 5^{9} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.038815298$ |
$0.444687310$ |
2.228520910 |
\( -\frac{6745520}{6561} a + \frac{2853296}{2187} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -143 a + 83\) , \( 767 a - 1062\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-143a+83\right){x}+767a-1062$ |
| 14400.9-c1 |
14400.9-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{3} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.201080352$ |
$2.762645847$ |
5.359798827 |
\( \frac{4864}{9} a - \frac{1792}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 4\) , \( 5 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-4\right){x}+5a-3$ |
| 14400.9-c2 |
14400.9-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{10} \cdot 5^{3} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.201080352$ |
$1.381322923$ |
5.359798827 |
\( -\frac{218384}{81} a + \frac{40352}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -7 a + 31\) , \( 19 a + 34\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a+31\right){x}+19a+34$ |
| 14400.9-d1 |
14400.9-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{10} \cdot 5^{3} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.295731021$ |
$2.337565592$ |
3.334911625 |
\( -\frac{15104}{81} a + \frac{512}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 4\) , \( 3 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-4\right){x}+3a+6$ |
| 14400.9-d2 |
14400.9-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 5^{3} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.591462042$ |
$1.168782796$ |
3.334911625 |
\( \frac{2838544}{9} a + \frac{125168}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -22 a - 89\) , \( 155 a + 247\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-22a-89\right){x}+155a+247$ |
| 14400.9-e1 |
14400.9-e |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{6} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 2 \) |
$1$ |
$1.415850985$ |
1.707580537 |
\( 1024 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -11 a + 14\) , \( -22 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a+14\right){x}-22a+1$ |
| 14400.9-f1 |
14400.9-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{10} \cdot 5^{9} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.045391113$ |
2.521578241 |
\( -\frac{15104}{81} a + \frac{512}{27} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 13 a - 19\) , \( -62 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(13a-19\right){x}-62a-48$ |
| 14400.9-f2 |
14400.9-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 5^{9} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.522695556$ |
2.521578241 |
\( \frac{2838544}{9} a + \frac{125168}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 308 a - 284\) , \( -2668 a - 796\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(308a-284\right){x}-2668a-796$ |
| 14400.9-g1 |
14400.9-g |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{9} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.177849306$ |
$1.235492782$ |
7.020266251 |
\( \frac{4864}{9} a - \frac{1792}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 13 a - 19\) , \( -48 a + 39\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(13a-19\right){x}-48a+39$ |
| 14400.9-g2 |
14400.9-g |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{10} \cdot 5^{9} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.355698613$ |
$0.617746391$ |
7.020266251 |
\( -\frac{218384}{81} a + \frac{40352}{27} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -82 a - 29\) , \( -455 a + 233\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-82a-29\right){x}-455a+233$ |
| 14400.9-h1 |
14400.9-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{9} \cdot 5^{16} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.652378473$ |
$0.284925431$ |
7.291558160 |
\( \frac{5153719856}{263671875} a - \frac{3651420368}{87890625} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -102 a + 111\) , \( 461 a + 5561\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-102a+111\right){x}+461a+5561$ |
| 14400.9-h2 |
14400.9-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{11} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.326189236$ |
$0.569850862$ |
7.291558160 |
\( -\frac{22006210816}{2278125} a + \frac{15720821248}{759375} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 128 a + 76\) , \( -85 a + 1418\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(128a+76\right){x}-85a+1418$ |
| 14400.9-i1 |
14400.9-i |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{8} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.975471119$ |
4.705849741 |
\( \frac{135568}{25} a - \frac{174112}{25} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 36 a - 60\) , \( -168 a + 104\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(36a-60\right){x}-168a+104$ |
| 14400.9-i2 |
14400.9-i |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{7} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.950942239$ |
4.705849741 |
\( -\frac{256}{5} a - \frac{2816}{5} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 5\) , \( -12 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-5\right){x}-12a+2$ |
| 14400.9-j1 |
14400.9-j |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{10} \cdot 5^{3} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.988702110$ |
4.796929978 |
\( \frac{1035520}{81} a - \frac{469504}{27} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 9 a + 9\) , \( 10 a - 52\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(9a+9\right){x}+10a-52$ |
| 14400.9-j2 |
14400.9-j |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.9 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{14} \cdot 5^{3} \) |
$3.24658$ |
$(a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.994351055$ |
4.796929978 |
\( -\frac{6745520}{6561} a + \frac{2853296}{2187} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a + 44\) , \( -60 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+44\right){x}-60a-12$ |
*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.
