| 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 |
| 34596.5-a1 |
34596.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34596.5 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{14} \cdot 3^{8} \cdot 31^{4} \) |
$4.04195$ |
$(-a), (a-1), (-3a+4), (3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.903441372$ |
2.179182584 |
\( \frac{1644811004447}{2779857792} a - \frac{3470748847849}{1389928896} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -34 a - 2\) , \( -144 a + 180\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-34a-2\right){x}-144a+180$ |
| 34596.5-b1 |
34596.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34596.5 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 31^{4} \) |
$4.04195$ |
$(-a), (a-1), (-3a+4), (3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$0.863840638$ |
0.520915504 |
\( \frac{83263722948091}{14478426} a + \frac{250680638394335}{14478426} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 134 a - 290\) , \( -1146 a + 1308\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(134a-290\right){x}-1146a+1308$ |
| 34596.5-c1 |
34596.5-c |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34596.5 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 31^{4} \) |
$4.04195$ |
$(-a), (a-1), (-3a+4), (3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$0.863840638$ |
0.520915504 |
\( -\frac{83263722948091}{14478426} a + \frac{55657393557071}{2413071} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -135 a - 156\) , \( 1145 a + 162\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-135a-156\right){x}+1145a+162$ |
| 34596.5-d1 |
34596.5-d |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34596.5 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{14} \cdot 3^{8} \cdot 31^{4} \) |
$4.04195$ |
$(-a), (a-1), (-3a+4), (3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.903441372$ |
2.179182584 |
\( -\frac{1644811004447}{2779857792} a - \frac{1765562230417}{926619264} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 35 a - 34\) , \( 109 a + 73\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(35a-34\right){x}+109a+73$ |
| 34596.5-e1 |
34596.5-e |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34596.5 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{2} \cdot 3^{22} \cdot 31^{2} \) |
$4.04195$ |
$(-a), (a-1), (-3a+4), (3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$0.856430089$ |
0.516446775 |
\( -\frac{64432972729}{10983114} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -83\) , \( -369\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-83{x}-369$ |
| 34596.5-f1 |
34596.5-f |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34596.5 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 31^{10} \) |
$4.04195$ |
$(-a), (a-1), (-3a+4), (3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 5^{2} \) |
$1$ |
$0.349000955$ |
5.261387361 |
\( -\frac{300238092661681}{171774906} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1395\) , \( -20181\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1395{x}-20181$ |
| 34596.5-f2 |
34596.5-f |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34596.5 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{10} \cdot 3^{10} \cdot 31^{2} \) |
$4.04195$ |
$(-a), (a-1), (-3a+4), (3a+1), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{3} \) |
$1$ |
$1.745004775$ |
5.261387361 |
\( \frac{371694959}{241056} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 15\) , \( 9\bigr] \) |
${y}^2+{x}{y}={x}^{3}+15{x}+9$ |
| 34596.5-g1 |
34596.5-g |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34596.5 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{14} \cdot 3^{2} \cdot 31^{2} \) |
$4.04195$ |
$(-a), (a-1), (-3a+4), (3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 7 \) |
$1$ |
$2.371857003$ |
10.01198512 |
\( -\frac{498677257}{11904} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -17\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-17{x}-28$ |
*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.
