| 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 |
| 92416.1-d1 |
92416.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{30} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.472595983$ |
$0.852647549$ |
6.447324923 |
\( -\frac{413493625}{152} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 248\) , \( 1424 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+248{x}+1424i$ |
| 5776.2-c1 |
5776.2-c |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5776.2 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{18} \cdot 19^{2} \) |
$2.20338$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.278258698$ |
$1.705295099$ |
2.684251981 |
\( -\frac{413493625}{152} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -62\) , \( 178\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-62{x}+178$ |
| 722.1-d1 |
722.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
722.1 |
\( 2 \cdot 19^{2} \) |
\( 2^{18} \cdot 19^{2} \) |
$2.26923$ |
$(2,a), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.278258698$ |
$3.410590199$ |
4.649260813 |
\( -\frac{413493625}{152} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -57\) , \( 241\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-57{x}+241$ |
| 722.2-a1 |
722.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
722.2 |
\( 2 \cdot 19^{2} \) |
\( 2^{18} \cdot 19^{2} \) |
$3.46631$ |
$(2,a), (19,a+9), (19,a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$0.278258698$ |
$3.410590199$ |
1.014551885 |
\( -\frac{413493625}{152} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -53\) , \( 243\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-53{x}+243$ |
| 722.2-d1 |
722.2-d |
$3$ |
$9$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
722.2 |
\( 2 \cdot 19^{2} \) |
\( 2^{18} \cdot 19^{2} \) |
$4.34524$ |
$(2,a), (19,a+4), (19,a+15)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.790477574$ |
$3.410590199$ |
13.79491392 |
\( -\frac{413493625}{152} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -52\) , \( 296\bigr] \) |
${y}^2+a{x}{y}={x}^3-52{x}+296$ |
| 722.1-a1 |
722.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
722.1 |
\( 2 \cdot 19^{2} \) |
\( 2^{18} \cdot 19^{2} \) |
$5.07415$ |
$(2,a), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1.571058862$ |
$3.410590199$ |
7.826207461 |
\( -\frac{413493625}{152} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -23\) , \( 349\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-23{x}+349$ |
| 38.1-b1 |
38.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-38}) \) |
$2$ |
$[0, 1]$ |
38.1 |
\( 2 \cdot 19 \) |
\( 2^{18} \cdot 19^{2} \) |
$2.73531$ |
$(2,a), (19,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.215560213$ |
$3.410590199$ |
5.724632144 |
\( -\frac{413493625}{152} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -19\) , \( 351\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-19{x}+351$ |
| 38.1-b1 |
38.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-190}) \) |
$2$ |
$[0, 1]$ |
38.1 |
\( 2 \cdot 19 \) |
\( 2^{18} \cdot 19^{2} \) |
$6.11633$ |
$(2,a), (19,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$4$ |
\( 2^{2} \) |
$0.278258698$ |
$6.821180399$ |
2.203187540 |
\( -\frac{413493625}{152} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 690\) , \( -2798\bigr] \) |
${y}^2+a{x}{y}={x}^3+690{x}-2798$ |
| 722.1-b1 |
722.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
722.1 |
\( 2 \cdot 19^{2} \) |
\( 2^{6} \cdot 19^{2} \) |
$1.31014$ |
$(a), (19)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.278258698$ |
$32.17041206$ |
1.406623475 |
\( -\frac{413493625}{152} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -16\) , \( 22\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-16{x}+22$ |
*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.
