| 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-a1 |
72.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{10} \) |
$1.27520$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.097728854$ |
$10.18034972$ |
1.624687623 |
\( -\frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -14 a + 36\) , \( 52 a - 127\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-14a+36\right){x}+52a-127$ |
| 72.1-a2 |
72.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$1.27520$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.195457709$ |
$20.36069944$ |
1.624687623 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -23 a - 60\) , \( 70 a + 170\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-23a-60\right){x}+70a+170$ |
| 72.1-b1 |
72.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{10} \) |
$1.27520$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.377869350$ |
1.787257678 |
\( \frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a - 12\) , \( 18 a - 45\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(6a-12\right){x}+18a-45$ |
| 72.1-b2 |
72.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$1.27520$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.755738700$ |
1.787257678 |
\( -\frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -20 a - 45\) , \( 53 a + 130\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-20a-45\right){x}+53a+130$ |
| 72.1-c1 |
72.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{10} \) |
$1.27520$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.097728854$ |
$10.18034972$ |
1.624687623 |
\( \frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 14 a + 36\) , \( -52 a - 127\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(14a+36\right){x}-52a-127$ |
| 72.1-c2 |
72.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$1.27520$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.195457709$ |
$20.36069944$ |
1.624687623 |
\( -\frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 23 a - 60\) , \( -70 a + 170\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(23a-60\right){x}-70a+170$ |
| 72.1-d1 |
72.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{10} \) |
$1.27520$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.377869350$ |
1.787257678 |
\( -\frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -6 a - 12\) , \( -18 a - 45\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-6a-12\right){x}-18a-45$ |
| 72.1-d2 |
72.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$1.27520$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.755738700$ |
1.787257678 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 20 a - 45\) , \( -53 a + 130\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(20a-45\right){x}-53a+130$ |
*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.
