| 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-a3 |
2304.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{4} \) |
$1.75107$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.319732820$ |
$4.292588069$ |
1.940981656 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2\) , \( -2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+2{x}-2$ |
| 2304.2-h3 |
2304.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{4} \) |
$1.75107$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.292588069$ |
3.035318132 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2\) , \( 2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+2{x}+2$ |
| 3456.2-d3 |
3456.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.2 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{10} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 2\) , \( 2 a - 10\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-2\right){x}+2a-10$ |
| 3456.2-e3 |
3456.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.2 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{10} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 2\) , \( -2 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-2\right){x}-2a+10$ |
| 3456.3-d3 |
3456.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{10} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 2\) , \( -2 a - 10\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-2\right){x}-2a-10$ |
| 3456.3-e3 |
3456.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{10} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 2\) , \( 2 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-2\right){x}+2a+10$ |
| 9216.2-j3 |
9216.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.901525282$ |
$3.035318132$ |
3.869876671 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -4\) , \( -4 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-4{x}-4a$ |
| 9216.2-r3 |
9216.2-r |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.901525282$ |
$3.035318132$ |
3.869876671 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -4\) , \( 4 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-4{x}+4a$ |
| 20736.3-b3 |
20736.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{16} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.395445231$ |
$1.430862689$ |
6.401611099 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( -38\bigr] \) |
${y}^2={x}^{3}+15{x}-38$ |
| 20736.3-v3 |
20736.3-v |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{16} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.603762616$ |
$1.430862689$ |
4.886964317 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( 38\bigr] \) |
${y}^2={x}^{3}+15{x}+38$ |
| 27648.2-h3 |
27648.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.780153827$ |
$1.752441741$ |
3.866952399 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a + 3\) , \( 13 a + 11\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a+3\right){x}+13a+11$ |
| 27648.2-bp3 |
27648.2-bp |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.752441741$ |
2.478326877 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a + 3\) , \( -13 a - 11\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a+3\right){x}-13a-11$ |
| 27648.3-s3 |
27648.3-s |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.780153827$ |
$1.752441741$ |
3.866952399 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a + 3\) , \( -13 a + 11\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a+3\right){x}-13a+11$ |
| 27648.3-bc3 |
27648.3-bc |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{10} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.752441741$ |
2.478326877 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 6 a + 3\) , \( 13 a - 11\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(6a+3\right){x}+13a-11$ |
*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.
