| 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-a6 |
72.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.73624$ |
$(a), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$37.20447790$ |
0.822110581 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -17\) , \( 27\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-17{x}+27$ |
| 144.1-b6 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.683508517$ |
1.004711853 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -17\) , \( -28\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-17{x}-28$ |
| 648.1-a6 |
648.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.27520$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.894502839$ |
1.339615804 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -145\) , \( -743\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-145{x}-743$ |
| 1296.1-b6 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.539636932$ |
$12.40149263$ |
2.366086572 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -144\) , \( 598\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-144{x}+598$ |
| 2304.1-c6 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.070944103$ |
$7.270694035$ |
2.752945917 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -128 a - 192\) , \( -1100 a - 1540\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-128a-192\right){x}-1100a-1540$ |
| 2304.1-s6 |
2304.1-s |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.070944103$ |
$7.270694035$ |
2.752945917 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -128 a - 192\) , \( 1100 a + 1540\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-128a-192\right){x}+1100a+1540$ |
| 3528.2-d6 |
3528.2-d |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{6} \) |
$1.94790$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.789108905$ |
$5.496128079$ |
3.066752947 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 64 a - 145\) , \( 605 a - 688\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(64a-145\right){x}+605a-688$ |
| 3528.3-d6 |
3528.3-d |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3528.3 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{6} \) |
$1.94790$ |
$(a), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.789108905$ |
$5.496128079$ |
3.066752947 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -64 a - 145\) , \( -605 a - 688\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-64a-145\right){x}-605a-688$ |
*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.
