| 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 |
| 2304.2-a1 |
2304.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{5} \) |
$1.75107$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.639465641$ |
$2.146294034$ |
1.940981656 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 10 a + 22\) , \( 20 a - 46\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(10a+22\right){x}+20a-46$ |
| 2304.2-h1 |
2304.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{5} \) |
$1.75107$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.146294034$ |
3.035318132 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 10 a + 22\) , \( -20 a + 46\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(10a+22\right){x}-20a+46$ |
| 3456.2-d1 |
3456.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.2 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{7} \cdot 3^{11} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 8 a - 15\) , \( -26 a + 16\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(8a-15\right){x}-26a+16$ |
| 3456.2-e1 |
3456.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.2 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{7} \cdot 3^{11} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 8 a - 15\) , \( 26 a - 15\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-15\right){x}+26a-15$ |
| 3456.3-d1 |
3456.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{7} \cdot 3^{11} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -13 a + 5\) , \( -9 a + 21\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-13a+5\right){x}-9a+21$ |
| 3456.3-e1 |
3456.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{7} \cdot 3^{11} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -13 a + 5\) , \( 9 a - 20\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-13a+5\right){x}+9a-20$ |
| 9216.2-j1 |
9216.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{25} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.803050564$ |
$1.517659066$ |
3.869876671 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -20 a - 44\) , \( -92 a - 80\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-20a-44\right){x}-92a-80$ |
| 9216.2-r1 |
9216.2-r |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{25} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.803050564$ |
$1.517659066$ |
3.869876671 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a - 44\) , \( 92 a + 80\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-20a-44\right){x}+92a+80$ |
| 20736.3-b1 |
20736.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{17} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.395445231$ |
$0.715431344$ |
6.401611099 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 90 a + 195\) , \( 630 a - 1046\bigr] \) |
${y}^2={x}^{3}+\left(90a+195\right){x}+630a-1046$ |
| 20736.3-v1 |
20736.3-v |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{17} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.301881308$ |
$0.715431344$ |
4.886964317 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 90 a + 195\) , \( -630 a + 1046\bigr] \) |
${y}^2={x}^{3}+\left(90a+195\right){x}-630a+1046$ |
| 27648.2-h1 |
27648.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.560307655$ |
$0.876220870$ |
3.866952399 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -66 a + 123\) , \( 313 a + 707\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-66a+123\right){x}+313a+707$ |
| 27648.2-bp1 |
27648.2-bp |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.876220870$ |
2.478326877 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -66 a + 123\) , \( -313 a - 707\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-66a+123\right){x}-313a-707$ |
| 27648.3-s1 |
27648.3-s |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.390076913$ |
$0.876220870$ |
3.866952399 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 106 a - 37\) , \( -433 a - 253\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(106a-37\right){x}-433a-253$ |
| 27648.3-bc1 |
27648.3-bc |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{25} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.876220870$ |
2.478326877 |
\( -\frac{4137500}{81} a - \frac{12439000}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 106 a - 37\) , \( 433 a + 253\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(106a-37\right){x}+433a+253$ |
*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.
