| 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 |
| 144.1-a2 |
144.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.95776$ |
$(2,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 1 \) |
$2.249823046$ |
$7.270694035$ |
2.586391323 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2+{x}$ |
| 24.1-b2 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{14} \) |
$2.16662$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.249823046$ |
$7.270694035$ |
2.986507453 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -7\bigr] \) |
${y}^2={x}^3+6{x}-7$ |
| 72.1-c2 |
72.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-70}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{12} \) |
$4.35563$ |
$(2,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$2.249823046$ |
$7.270694035$ |
7.820512267 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 33\) , \( -78\bigr] \) |
${y}^2={x}^3+{x}^2+33{x}-78$ |
| 72.2-a2 |
72.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-110}) \) |
$2$ |
$[0, 1]$ |
72.2 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{12} \) |
$5.46007$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.249823046$ |
$7.270694035$ |
3.119305301 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 81\) , \( -372\bigr] \) |
${y}^2={x}^3-{x}^2+81{x}-372$ |
| 72.1-b2 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-190}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 19^{12} \) |
$7.17593$ |
$(2,a), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$7.031124862$ |
$14.54138807$ |
14.83487428 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 241\) , \( -1698\bigr] \) |
${y}^2={x}^3+{x}^2+241{x}-1698$ |
| 72.2-b2 |
72.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-230}) \) |
$2$ |
$[0, 1]$ |
72.2 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 23^{12} \) |
$7.89524$ |
$(2,a), (3,a+1), (3,a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$13.65710210$ |
$14.54138807$ |
13.09484925 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 353\) , \( -3272\bigr] \) |
${y}^2={x}^3-{x}^2+353{x}-3272$ |
| 72.1-f2 |
72.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.249823046$ |
$18.60223895$ |
1.654335513 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
*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.
