| 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 |
| 3025.2-b2 |
3025.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{2} \) |
$2.19794$ |
$(-a-1), (a-2), (-2a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.223573260$ |
$5.155203162$ |
2.780092776 |
\( \frac{206103}{125} a + \frac{264299}{125} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -a - 2\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-a-2\right){x}$ |
| 15125.2-b1 |
15125.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
15125.2 |
\( 5^{3} \cdot 11^{2} \) |
\( 5^{10} \cdot 11^{2} \) |
$3.28669$ |
$(-a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.471735662$ |
$2.305476941$ |
5.246662546 |
\( \frac{206103}{125} a + \frac{264299}{125} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -5 a + 10\) , \( -9 a - 5\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+10\right){x}-9a-5$ |
| 15125.3-b1 |
15125.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
15125.3 |
\( 5^{3} \cdot 11^{2} \) |
\( 5^{10} \cdot 11^{2} \) |
$3.28669$ |
$(-a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.157245220$ |
$2.305476941$ |
5.246662546 |
\( \frac{206103}{125} a + \frac{264299}{125} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 4 a - 8\) , \( -7 a + 7\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(4a-8\right){x}-7a+7$ |
| 27225.2-d1 |
27225.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.2 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{4} \cdot 11^{8} \) |
$3.80695$ |
$(-a), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$4$ |
\( 3^{2} \) |
$1$ |
$0.897405682$ |
2.164623951 |
\( \frac{206103}{125} a + \frac{264299}{125} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -10 a - 63\) , \( 57 a + 160\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-10a-63\right){x}+57a+160$ |
| 27225.8-d1 |
27225.8-d |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.8 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{4} \cdot 11^{8} \) |
$3.80695$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$0.897405682$ |
2.164623951 |
\( \frac{206103}{125} a + \frac{264299}{125} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -42 a + 7\) , \( 98 a - 218\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-42a+7\right){x}+98a-218$ |
*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.
