| 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 |
| 135.3-a1 |
135.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
135.3 |
\( 3^{3} \cdot 5 \) |
\( 3^{9} \cdot 5^{4} \) |
$1.01023$ |
$(-a), (a-1), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.983066162$ |
1.199237719 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -7 a - 2\) , \( 6 a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a-2\right){x}+6a+2$ |
| 405.5-a1 |
405.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
405.5 |
\( 3^{4} \cdot 5 \) |
\( 3^{21} \cdot 5^{4} \) |
$1.32953$ |
$(-a), (a-1), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$0.199009437$ |
$0.994355387$ |
1.909276988 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -53 a + 7\) , \( -160 a + 258\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-53a+7\right){x}-160a+258$ |
| 675.4-b1 |
675.4-b |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.4 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{9} \cdot 5^{10} \) |
$1.51064$ |
$(-a), (a-1), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.333801161$ |
$1.334067744$ |
2.148272491 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -3 a + 49\) , \( -94 a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+49\right){x}-94a-2$ |
| 2025.7-a1 |
2025.7-a |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2025.7 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{21} \cdot 5^{10} \) |
$1.98811$ |
$(-a), (a-1), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.444689248$ |
2.145261649 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -30 a + 453\) , \( 2123 a - 466\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-30a+453\right){x}+2123a-466$ |
| 3375.7-c1 |
3375.7-c |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.7 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{9} \cdot 5^{10} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.122278091$ |
$1.334067744$ |
4.721733021 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 9 a - 51\) , \( -44 a + 146\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(9a-51\right){x}-44a+146$ |
| 10125.11-e3 |
10125.11-e |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
10125.11 |
\( 3^{4} \cdot 5^{3} \) |
\( 3^{21} \cdot 5^{10} \) |
$2.97292$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.444689248$ |
2.145261649 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 82 a - 459\) , \( 1106 a - 3481\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(82a-459\right){x}+1106a-3481$ |
| 16335.3-b3 |
16335.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16335.3 |
\( 3^{3} \cdot 5 \cdot 11^{2} \) |
\( 3^{15} \cdot 5^{4} \cdot 11^{6} \) |
$3.35054$ |
$(-a), (a-1), (-a-1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.748367044$ |
$0.519285165$ |
3.749507319 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -136 a - 165\) , \( 1134 a + 559\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-136a-165\right){x}+1134a+559$ |
| 16875.8-i3 |
16875.8-i |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.8 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{9} \cdot 5^{16} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.668086496$ |
$0.596613232$ |
3.845733729 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -144 a + 21\) , \( 892 a - 1078\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-144a+21\right){x}+892a-1078$ |
| 34560.3-e3 |
34560.3-e |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34560.3 |
\( 2^{8} \cdot 3^{3} \cdot 5 \) |
\( 2^{24} \cdot 3^{9} \cdot 5^{4} \) |
$4.04090$ |
$(-a), (a-1), (-a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.774612807$ |
$0.745766540$ |
2.786834691 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -92 a + 12\) , \( -388 a + 436\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-92a+12\right){x}-388a+436$ |
| 34560.3-k3 |
34560.3-k |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34560.3 |
\( 2^{8} \cdot 3^{3} \cdot 5 \) |
\( 2^{24} \cdot 3^{15} \cdot 5^{4} \) |
$4.04090$ |
$(-a), (a-1), (-a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.430568512$ |
2.077140660 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 198 a + 237\) , \( 871 a - 3874\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(198a+237\right){x}+871a-3874$ |
| 34560.3-bg3 |
34560.3-bg |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34560.3 |
\( 2^{8} \cdot 3^{3} \cdot 5 \) |
\( 2^{24} \cdot 3^{15} \cdot 5^{4} \) |
$4.04090$ |
$(-a), (a-1), (-a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.847666828$ |
$0.430568512$ |
5.282169709 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 198 a + 237\) , \( -871 a + 3874\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(198a+237\right){x}-871a+3874$ |
| 49005.5-c3 |
49005.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
49005.5 |
\( 3^{4} \cdot 5 \cdot 11^{2} \) |
\( 3^{15} \cdot 5^{4} \cdot 11^{6} \) |
$4.40956$ |
$(-a), (a-1), (-a-1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.839021773$ |
$0.519285165$ |
4.203710339 |
\( -\frac{8044322507}{455625} a + \frac{677729048}{151875} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -182 a + 208\) , \( 387 a - 2397\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-182a+208\right){x}+387a-2397$ |
*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.
