| 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 |
| 30276.2-a1 |
30276.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30276.2 |
\( 2^{2} \cdot 3^{2} \cdot 29^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 29^{2} \) |
$3.90939$ |
$(-a), (a-1), (2), (29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.340790346$ |
$3.667475200$ |
5.930505445 |
\( -\frac{13997521}{1566} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( -7\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}-7$ |
| 30276.2-b1 |
30276.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30276.2 |
\( 2^{2} \cdot 3^{2} \cdot 29^{2} \) |
\( 2^{26} \cdot 3^{2} \cdot 29^{2} \) |
$3.90939$ |
$(-a), (a-1), (2), (29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 13 \) |
$0.393476235$ |
$1.233279083$ |
7.608286788 |
\( -\frac{19968681097}{712704} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -56\) , \( -192\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-56{x}-192$ |
| 30276.2-c1 |
30276.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30276.2 |
\( 2^{2} \cdot 3^{2} \cdot 29^{2} \) |
\( 2^{22} \cdot 3^{42} \cdot 29^{2} \) |
$3.90939$ |
$(-a), (a-1), (2), (29)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \cdot 7^{2} \cdot 11 \) |
$0.209640478$ |
$0.047800804$ |
6.514225148 |
\( -\frac{50577879066661513}{621261297432576} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -7705\) , \( 1226492\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-7705{x}+1226492$ |
| 30276.2-c2 |
30276.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30276.2 |
\( 2^{2} \cdot 3^{2} \cdot 29^{2} \) |
\( 2^{66} \cdot 3^{14} \cdot 29^{6} \) |
$3.90939$ |
$(-a), (a-1), (2), (29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \cdot 7^{2} \cdot 11 \) |
$0.069880159$ |
$0.015933601$ |
6.514225148 |
\( \frac{36079072622241241607}{458176313589497856} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 68840\) , \( -31810330\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+68840{x}-31810330$ |
| 30276.2-d1 |
30276.2-d |
$2$ |
$7$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30276.2 |
\( 2^{2} \cdot 3^{2} \cdot 29^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 29^{14} \) |
$3.90939$ |
$(-a), (a-1), (2), (29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.3 |
$1$ |
\( 7 \) |
$6.401855163$ |
$0.141523007$ |
7.648822501 |
\( -\frac{30526075007211889}{103499257854} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -6511\) , \( -203353\bigr] \) |
${y}^2+{x}{y}={x}^{3}-6511{x}-203353$ |
| 30276.2-d2 |
30276.2-d |
$2$ |
$7$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30276.2 |
\( 2^{2} \cdot 3^{2} \cdot 29^{2} \) |
\( 2^{14} \cdot 3^{14} \cdot 29^{2} \) |
$3.90939$ |
$(-a), (a-1), (2), (29)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{3} \) |
$0.914550737$ |
$0.990661053$ |
7.648822501 |
\( -\frac{117649}{8118144} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1\) , \( 137\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}+137$ |
| 30276.2-e1 |
30276.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30276.2 |
\( 2^{2} \cdot 3^{2} \cdot 29^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 29^{2} \) |
$3.90939$ |
$(-a), (a-1), (2), (29)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.354239377$ |
$4.198874530$ |
11.92194641 |
\( \frac{12167}{1392} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( -2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2$ |
| 30276.2-e2 |
30276.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30276.2 |
\( 2^{2} \cdot 3^{2} \cdot 29^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 29^{8} \) |
$3.90939$ |
$(-a), (a-1), (2), (29)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$9.416957511$ |
$1.049718632$ |
11.92194641 |
\( \frac{13430356633}{4243686} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -50\) , \( 86\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-50{x}+86$ |
| 30276.2-e3 |
30276.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30276.2 |
\( 2^{2} \cdot 3^{2} \cdot 29^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 29^{4} \) |
$3.90939$ |
$(-a), (a-1), (2), (29)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$4.708478755$ |
$2.099437265$ |
11.92194641 |
\( \frac{822656953}{30276} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -20\) , \( -34\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-20{x}-34$ |
| 30276.2-e4 |
30276.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
30276.2 |
\( 2^{2} \cdot 3^{2} \cdot 29^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 29^{2} \) |
$3.90939$ |
$(-a), (a-1), (2), (29)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.354239377$ |
$1.049718632$ |
11.92194641 |
\( \frac{3279392280793}{4698} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -310\) , \( -2122\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-310{x}-2122$ |
*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.
