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-a2 |
72.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$0.73624$ |
$(a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.325279868$ |
0.822110581 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 3\) , \( -23\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+3{x}-23$ |
144.1-b2 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$5.683508517$ |
1.004711853 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( 22\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+3{x}+22$ |
648.1-a2 |
648.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{28} \) |
$1.27520$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.894502839$ |
1.339615804 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 35\) , \( 607\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+35{x}+607$ |
1296.1-b2 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{28} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.079273864$ |
$0.775093289$ |
2.366086572 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 36\) , \( -572\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+36{x}-572$ |
2304.1-c2 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.141888207$ |
$1.817673508$ |
2.752945917 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 32 a + 48\) , \( 900 a + 1260\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(32a+48\right){x}+900a+1260$ |
2304.1-s2 |
2304.1-s |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.141888207$ |
$1.817673508$ |
2.752945917 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 32 a + 48\) , \( -900 a - 1260\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a+48\right){x}-900a-1260$ |
3528.2-d2 |
3528.2-d |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 7^{6} \) |
$1.94790$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.578217810$ |
$1.374032019$ |
3.066752947 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -16 a + 35\) , \( -495 a + 562\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-16a+35\right){x}-495a+562$ |
3528.3-d2 |
3528.3-d |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3528.3 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 7^{6} \) |
$1.94790$ |
$(a), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.578217810$ |
$1.374032019$ |
3.066752947 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 16 a + 35\) , \( 495 a + 562\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(16a+35\right){x}+495a+562$ |
*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.