| 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 |
| 507.2-a2 |
507.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$0.73443$ |
$(-2a+1), (-4a+1), (4a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.141291953$ |
$3.780590085$ |
0.616802873 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 1521.2-a2 |
1521.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1521.2 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$1.11609$ |
$(-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.780590085$ |
1.890295042 |
\( \frac{10218313}{1521} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -4\) , \( 5\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-4{x}+5$ |
| 1521.1-a2 |
1521.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$1.47645$ |
$(3), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.212873284$ |
$3.780590085$ |
3.162038233 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 1521.2-a2 |
1521.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1521.2 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$1.57840$ |
$(-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.780590085$ |
1.336640443 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 1521.2-a2 |
1521.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1521.2 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$1.85083$ |
$(-a), (a-1), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.780590085$ |
1.139890800 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 507.1-b2 |
507.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
507.1 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$1.64224$ |
$(3,a+1), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$3.780590085$ |
1.952288325 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 1521.1-a2 |
1521.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$2.43247$ |
$(3), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.669657180$ |
$3.780590085$ |
3.182792199 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 1521.5-a2 |
1521.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
1521.5 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$2.67630$ |
$(3,a), (3,a+2), (13,a+4), (13,a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.153155305$ |
$3.780590085$ |
3.636164026 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 507.1-b2 |
507.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
507.1 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$2.07729$ |
$(3,a), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$3.780590085$ |
1.543419439 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 1521.1-a2 |
1521.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$3.10707$ |
$(3), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$8.742950383$ |
$3.780590085$ |
5.936585923 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 39.1-b4 |
39.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-39}) \) |
$2$ |
$[0, 1]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{4} \cdot 13^{4} \) |
$1.39456$ |
$(3,a+1), (13,a+6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$3.780590085$ |
2.421515642 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 1521.2-a2 |
1521.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
1521.2 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$3.65936$ |
$(a+1), (a-2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$3.780590085$ |
2.306138332 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 507.2-a2 |
507.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-51}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$3.02814$ |
$(3,a+1), (a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1.025761881$ |
$3.780590085$ |
4.344212354 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 117.1-b2 |
117.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
117.1 |
\( 3^{2} \cdot 13 \) |
\( 3^{4} \cdot 13^{4} \) |
$2.11927$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$3.222666247$ |
$3.780590085$ |
3.379117126 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 1521.1-a2 |
1521.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$4.56781$ |
$(3), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$8.002452540$ |
$3.780590085$ |
3.696113482 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 507.1-c2 |
507.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
507.1 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$3.88625$ |
$(3,a), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$3.780590085$ |
3.299969569 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 507.2-b2 |
507.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$3.95503$ |
$(3,a+1), (13,a+5), (13,a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1.300503768$ |
$3.780590085$ |
4.216980248 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 117.1-b2 |
117.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
117.1 |
\( 3^{2} \cdot 13 \) |
\( 3^{4} \cdot 13^{4} \) |
$2.80353$ |
$(13,a+6), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$4.445191832$ |
$3.780590085$ |
3.523379298 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 117.2-a2 |
117.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
117.2 |
\( 3^{2} \cdot 13 \) |
\( 3^{4} \cdot 13^{4} \) |
$2.99710$ |
$(3,a+1), (3,a+2), (13,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.780590085$ |
0.741434716 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 507.1-d2 |
507.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
507.1 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$4.46737$ |
$(3,a+1), (13)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$16.72414855$ |
$7.561180171$ |
12.00251103 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 507.2-c2 |
507.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$4.64495$ |
$(3,a), (13,a+3), (13,a+10)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$3.089065020$ |
$3.780590085$ |
8.528762184 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 1521.1-a2 |
1521.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$7.12467$ |
$(3), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$16.18733146$ |
$3.780590085$ |
4.793371051 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 39.1-c2 |
39.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-195}) \) |
$2$ |
$[0, 1]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{4} \cdot 13^{4} \) |
$3.11833$ |
$(3,a+1), (13,a+6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$3.780590085$ |
1.082934717 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 39.1-b2 |
39.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-78}) \) |
$2$ |
$[0, 1]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{4} \cdot 13^{4} \) |
$3.94441$ |
$(3,a), (13,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$3.780590085$ |
0.856135065 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 39.1-c2 |
39.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-663}) \) |
$2$ |
$[0, 1]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{4} \cdot 13^{4} \) |
$5.74992$ |
$(3,a+1), (13,a+6)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$3.868603552$ |
$7.561180171$ |
9.088182424 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-4{x}-5$ |
| 1521.1-a2 |
1521.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$1.24783$ |
$(3), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$10.93460483$ |
1.222525986 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 1521.1-b2 |
1521.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$1.57840$ |
$(3), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$10.93460483$ |
0.966491653 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 507.1-b3 |
507.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
507.1 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$1.46886$ |
$(a), (a+4), (a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.93460483$ |
1.578274261 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 117.1-b3 |
117.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
117.1 |
\( 3^{2} \cdot 13 \) |
\( 3^{4} \cdot 13^{4} \) |
$1.05964$ |
$(-a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.633671859$ |
$10.93460483$ |
0.960872672 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 507.1-a2 |
507.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
507.1 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$1.94312$ |
$(-a+2), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.888578100$ |
$10.93460483$ |
2.253193030 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 507.1-d2 |
507.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
507.1 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$2.07729$ |
$(a+3), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.806034205$ |
$10.93460483$ |
4.247566269 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 507.1-a2 |
507.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
507.1 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$2.43583$ |
$(-2a+7), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$4.787005907$ |
$10.93460483$ |
4.555961975 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 1521.1-d2 |
1521.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1521.1 |
\( 3^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$4.06264$ |
$(a), (a-1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.704426362$ |
$10.93460483$ |
2.560020251 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 117.1-b2 |
117.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
117.1 |
\( 3^{2} \cdot 13 \) |
\( 3^{4} \cdot 13^{4} \) |
$2.36942$ |
$(13,a+6), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.93460483$ |
0.678135404 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 351.1-a3 |
351.1-a |
$4$ |
$4$ |
3.3.169.1 |
$3$ |
$[3, 0]$ |
351.1 |
\( 3^{3} \cdot 13 \) |
\( 3^{6} \cdot 13^{6} \) |
$3.08532$ |
$(-2a^2+3a+5), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$36.15801988$ |
2.086039609 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
*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.
