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 |
7425.5-f8 |
7425.5-f |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.5 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{19} \cdot 5^{15} \cdot 11 \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{3} \) |
$1$ |
$0.256794058$ |
1.238821148 |
\( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -385 a + 705\) , \( 2093 a + 5394\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-385a+705\right){x}+2093a+5394$ |
7425.8-h8 |
7425.8-h |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.8 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{19} \cdot 5^{15} \cdot 11 \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
$1.407799633$ |
$0.256794058$ |
5.232035875 |
\( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 137 a + 719\) , \( 3565 a - 5599\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(137a+719\right){x}+3565a-5599$ |
27225.5-d8 |
27225.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.5 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{13} \cdot 5^{15} \cdot 11^{7} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.661233752$ |
$0.134106323$ |
3.224221700 |
\( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -545 a + 3138\) , \( -27234 a + 3585\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-545a+3138\right){x}-27234a+3585$ |
37125.10-j8 |
37125.10-j |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.10 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{19} \cdot 5^{21} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.114841794$ |
3.324105959 |
\( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 2294 a - 2669\) , \( -44686 a + 23022\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(2294a-2669\right){x}-44686a+23022$ |
37125.11-g8 |
37125.11-g |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.11 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{19} \cdot 5^{21} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$4.286586173$ |
$0.114841794$ |
4.749688881 |
\( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -2430 a + 1949\) , \( -14391 a + 80030\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2430a+1949\right){x}-14391a+80030$ |
37125.6-i8 |
37125.6-i |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.6 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{19} \cdot 5^{21} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1.744089115$ |
$0.114841794$ |
5.797537023 |
\( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 1738 a + 2043\) , \( 6612 a - 75145\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1738a+2043\right){x}+6612a-75145$ |
37125.7-k8 |
37125.7-k |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.7 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{19} \cdot 5^{21} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.114841794$ |
3.324105959 |
\( \frac{1032777340820292487}{1427209716796875} a + \frac{3533183376724708442}{1427209716796875} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -1354 a - 2751\) , \( -39143 a - 13940\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-1354a-2751\right){x}-39143a-13940$ |
*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.