| 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 |
| 275.2-a3 |
275.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
275.2 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{8} \) |
$1.20689$ |
$(-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.409696668$ |
$1.770622110$ |
1.505168807 |
\( \frac{2749884201}{73205} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$ |
| 1375.2-a3 |
1375.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1375.2 |
\( 5^{3} \cdot 11 \) |
\( 5^{8} \cdot 11^{8} \) |
$1.80472$ |
$(-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.791846280$ |
1.910005093 |
\( \frac{2749884201}{73205} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -87 a + 58\) , \( -208 a + 572\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-87a+58\right){x}-208a+572$ |
| 1375.3-a3 |
1375.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1375.3 |
\( 5^{3} \cdot 11 \) |
\( 5^{8} \cdot 11^{8} \) |
$1.80472$ |
$(-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.791846280$ |
1.910005093 |
\( \frac{2749884201}{73205} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 87 a - 29\) , \( 208 a + 364\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(87a-29\right){x}+208a+364$ |
| 6875.3-a3 |
6875.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6875.3 |
\( 5^{4} \cdot 11 \) |
\( 5^{14} \cdot 11^{8} \) |
$2.69869$ |
$(-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.596122623$ |
$0.354124422$ |
2.036784674 |
\( \frac{2749884201}{73205} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -730\) , \( -7228\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-730{x}-7228$ |
| 22275.8-a3 |
22275.8-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.8 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{12} \cdot 5^{2} \cdot 11^{8} \) |
$3.62067$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.496724502$ |
$0.590207370$ |
5.657230102 |
\( \frac{2749884201}{73205} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -263\) , \( 1666\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-263{x}+1666$ |
| 27225.2-b3 |
27225.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.2 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{2} \cdot 11^{14} \) |
$3.80695$ |
$(-a), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.308225746$ |
1.486936948 |
\( \frac{2749884201}{73205} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 319 a - 962\) , \( 4895 a - 9540\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(319a-962\right){x}+4895a-9540$ |
| 27225.8-b3 |
27225.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.8 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{2} \cdot 11^{14} \) |
$3.80695$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.308225746$ |
1.486936948 |
\( \frac{2749884201}{73205} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -321 a - 641\) , \( -4896 a - 4644\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-321a-641\right){x}-4896a-4644$ |
*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.
