| 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 |
| 500.2-a1 |
500.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
500.2 |
\( 2^{2} \cdot 5^{3} \) |
\( 2^{2} \cdot 5^{8} \) |
$1.40145$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$0.742119047$ |
$4.189143611$ |
1.499762421 |
\( \frac{2632683}{6250} a - \frac{535861}{3125} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -3\) , \( -a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}-3{x}-a-2$ |
| 500.2-b1 |
500.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
500.2 |
\( 2^{2} \cdot 5^{3} \) |
\( 2^{2} \cdot 5^{14} \) |
$1.40145$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.467284925$ |
$1.873441976$ |
2.111619493 |
\( \frac{2632683}{6250} a - \frac{535861}{3125} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -7 a + 3\) , \( -3 a + 16\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a+3\right){x}-3a+16$ |
| 2500.3-e1 |
2500.3-e |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{14} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{3} \) |
$0.187131889$ |
$1.873441976$ |
3.382530227 |
\( \frac{2632683}{6250} a - \frac{535861}{3125} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 5 a\) , \( 11 a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+5a{x}+11a+1$ |
| 2500.3-f1 |
2500.3-f |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 5^{20} \) |
$2.09566$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.837828722$ |
2.020918916 |
\( \frac{2632683}{6250} a - \frac{535861}{3125} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -50\) , \( -81 a - 146\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-50{x}-81a-146$ |
| 32000.2-u1 |
32000.2-u |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{26} \cdot 5^{14} \) |
$3.96390$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.468360494$ |
2.259456037 |
\( \frac{2632683}{6250} a - \frac{535861}{3125} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -95 a + 55\) , \( 27 a - 1168\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-95a+55\right){x}+27a-1168$ |
| 32000.2-x1 |
32000.2-x |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{26} \cdot 5^{8} \) |
$3.96390$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.299138767$ |
$1.047285902$ |
7.556689921 |
\( \frac{2632683}{6250} a - \frac{535861}{3125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( a - 32\) , \( 35 a + 68\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(a-32\right){x}+35a+68$ |
| 40500.10-c1 |
40500.10-c |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40500.10 |
\( 2^{2} \cdot 3^{4} \cdot 5^{3} \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{8} \) |
$4.20435$ |
$(-a), (a-1), (-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.396381203$ |
1.684099097 |
\( \frac{2632683}{6250} a - \frac{535861}{3125} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -18\) , \( 10 a + 42\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}-18{x}+10a+42$ |
| 40500.10-bg1 |
40500.10-bg |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40500.10 |
\( 2^{2} \cdot 3^{4} \cdot 5^{3} \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{14} \) |
$4.20435$ |
$(-a), (a-1), (-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.624480658$ |
3.765760062 |
\( \frac{2632683}{6250} a - \frac{535861}{3125} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -54 a + 31\) , \( 44 a - 549\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-54a+31\right){x}+44a-549$ |
*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.
