| 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 |
| 500.3-a1 |
500.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
500.3 |
\( 2^{2} \cdot 5^{3} \) |
\( 2^{2} \cdot 5^{8} \) |
$1.40145$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$0.742119047$ |
$4.189143611$ |
1.499762421 |
\( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}$ |
| 500.3-b1 |
500.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
500.3 |
\( 2^{2} \cdot 5^{3} \) |
\( 2^{2} \cdot 5^{14} \) |
$1.40145$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.467284925$ |
$1.873441976$ |
2.111619493 |
\( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 6 a - 4\) , \( 2 a + 13\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(6a-4\right){x}+2a+13$ |
| 2500.3-c1 |
2500.3-c |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
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 |
\( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -7 a + 6\) , \( -12 a + 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a+6\right){x}-12a+13$ |
| 2500.3-g1 |
2500.3-g |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
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 |
\( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2 a - 48\) , \( 80 a - 226\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-48\right){x}+80a-226$ |
| 32000.3-m1 |
32000.3-m |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{26} \cdot 5^{14} \) |
$3.96390$ |
$(-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.468360494$ |
2.259456037 |
\( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 97 a - 41\) , \( -123 a - 1100\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(97a-41\right){x}-123a-1100$ |
| 32000.3-bc1 |
32000.3-bc |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{26} \cdot 5^{8} \) |
$3.96390$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.299138767$ |
$1.047285902$ |
7.556689921 |
\( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a - 31\) , \( -35 a + 103\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a-31\right){x}-35a+103$ |
| 40500.11-d1 |
40500.11-d |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40500.11 |
\( 2^{2} \cdot 3^{4} \cdot 5^{3} \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{8} \) |
$4.20435$ |
$(-a), (a-1), (-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.396381203$ |
1.684099097 |
\( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -18\) , \( -10 a + 52\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}-18{x}-10a+52$ |
| 40500.11-bg1 |
40500.11-bg |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40500.11 |
\( 2^{2} \cdot 3^{4} \cdot 5^{3} \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{14} \) |
$4.20435$ |
$(-a), (a-1), (-a-1), (a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.624480658$ |
3.765760062 |
\( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 54 a - 23\) , \( -44 a - 505\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(54a-23\right){x}-44a-505$ |
*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.
