| 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 |
| 34596.3-a1 |
34596.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
34596.3 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{4} \cdot 3^{9} \cdot 31^{8} \) |
$2.11084$ |
$(-2a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.209341173$ |
$0.448180036$ |
2.600086359 |
\( \frac{27357}{4} a + \frac{2559}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -378 a + 150\) , \( 1815 a - 2246\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-378a+150\right){x}+1815a-2246$ |
| 34596.3-b1 |
34596.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
34596.3 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{4} \cdot 3^{3} \cdot 31^{2} \) |
$2.11084$ |
$(-2a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.080738863$ |
$4.322091753$ |
3.223561561 |
\( \frac{27357}{4} a + \frac{2559}{2} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -2 a - 2\) , \( -6 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-2\right){x}-6a+1$ |
| 34596.3-c1 |
34596.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
34596.3 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 31^{10} \) |
$2.11084$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.212010738$ |
1.958471311 |
\( -\frac{340439}{144} a + \frac{208705}{144} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -662 a - 564\) , \( -8311 a - 8954\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-662a-564\right){x}-8311a-8954$ |
| 34596.3-d1 |
34596.3-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
34596.3 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{50} \cdot 3^{6} \cdot 31^{7} \) |
$2.11084$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$0.038204596$ |
2.205743407 |
\( \frac{936087656892551}{1040187392} a - \frac{833285178768245}{1040187392} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -82463 a + 118366\) , \( 6646969 a + 8461763\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-82463a+118366\right){x}+6646969a+8461763$ |
| 34596.3-d2 |
34596.3-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
34596.3 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 31^{7} \) |
$2.11084$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$0.955114912$ |
2.205743407 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 37 a + 16\) , \( 49 a + 23\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(37a+16\right){x}+49a+23$ |
| 34596.3-d3 |
34596.3-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
34596.3 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 31^{11} \) |
$2.11084$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.191022982$ |
2.205743407 |
\( -\frac{511363962461}{916132832} a + \frac{764718499383}{458066416} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 892 a - 1394\) , \( -11606 a + 2249\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(892a-1394\right){x}-11606a+2249$ |
*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.
