| 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 |
| 72.1-a7 |
72.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$0.73624$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$2.325279868$ |
0.822110581 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -97\) , \( -347\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-97{x}-347$ |
| 144.1-b7 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$22.73403407$ |
1.004711853 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -97\) , \( 346\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-97{x}+346$ |
| 648.1-a7 |
648.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{16} \) |
$1.27520$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$7.578011356$ |
1.339615804 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -865\) , \( 9355\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-865{x}+9355$ |
| 1296.1-b7 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{16} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$4.317095458$ |
$0.775093289$ |
2.366086572 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -864\) , \( -10220\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-864{x}-10220$ |
| 2304.1-c7 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.141888207$ |
$3.635347017$ |
2.752945917 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 768 a - 1152\) , \( 13860 a - 19404\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(768a-1152\right){x}+13860a-19404$ |
| 2304.1-s7 |
2304.1-s |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.141888207$ |
$3.635347017$ |
2.752945917 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 768 a - 1152\) , \( -13860 a + 19404\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(768a-1152\right){x}-13860a+19404$ |
| 3528.2-d7 |
3528.2-d |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 7^{6} \) |
$1.94790$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.578217810$ |
$2.748064039$ |
3.066752947 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 384 a - 865\) , \( -7623 a + 8662\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(384a-865\right){x}-7623a+8662$ |
| 3528.3-d7 |
3528.3-d |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3528.3 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 7^{6} \) |
$1.94790$ |
$(a), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.578217810$ |
$2.748064039$ |
3.066752947 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -384 a - 865\) , \( 7623 a + 8662\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-384a-865\right){x}+7623a+8662$ |
*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.
