| 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-a4 |
2304.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$1.75107$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.639465641$ |
$4.292588069$ |
1.940981656 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3{x}+3$ |
| 2304.2-h4 |
2304.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$1.75107$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.292588069$ |
3.035318132 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}-3$ |
| 3456.2-d4 |
3456.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.2 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{8} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a + 3\) , \( -3 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a+3\right){x}-3a+15$ |
| 3456.2-e4 |
3456.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.2 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{8} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a + 3\) , \( 3 a - 15\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a+3\right){x}+3a-15$ |
| 3456.3-d4 |
3456.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{8} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a + 3\) , \( 3 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a+3\right){x}+3a+15$ |
| 3456.3-e4 |
3456.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3456.3 |
\( 2^{7} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{8} \) |
$1.93788$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.478326877$ |
1.752441741 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 6 a + 3\) , \( -3 a - 15\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(6a+3\right){x}-3a-15$ |
| 9216.2-j4 |
9216.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{2} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.803050564$ |
$6.070636265$ |
3.869876671 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}$ |
| 9216.2-r4 |
9216.2-r |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{2} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.803050564$ |
$6.070636265$ |
3.869876671 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}$ |
| 20736.3-b4 |
20736.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{14} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.098861307$ |
$1.430862689$ |
6.401611099 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30\) , \( 52\bigr] \) |
${y}^2={x}^{3}-30{x}+52$ |
| 20736.3-v4 |
20736.3-v |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{14} \) |
$3.03295$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.207525233$ |
$1.430862689$ |
4.886964317 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -30\) , \( -52\bigr] \) |
${y}^2={x}^{3}-30{x}-52$ |
| 27648.2-h4 |
27648.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.560307655$ |
$3.504883482$ |
3.866952399 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 2\) , \( 3 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-2\right){x}+3a-2$ |
| 27648.2-bp4 |
27648.2-bp |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.504883482$ |
2.478326877 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 2\) , \( -3 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-2\right){x}-3a+2$ |
| 27648.3-s4 |
27648.3-s |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.560307655$ |
$3.504883482$ |
3.866952399 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 2\) , \( -3 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-2\right){x}-3a-2$ |
| 27648.3-bc4 |
27648.3-bc |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{8} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.504883482$ |
2.478326877 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 2\) , \( 3 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-2\right){x}+3a+2$ |
*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.
