| 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 |
| 27075.2-c2 |
27075.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
27075.2 |
\( 3 \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{20} \cdot 5^{4} \cdot 19^{2} \) |
$1.98537$ |
$(-2a+1), (-5a+3), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.134827177$ |
$0.788766240$ |
2.455981678 |
\( \frac{48587168449}{28048275} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 76 a\) , \( -19\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+76a{x}-19$ |
| 81225.2-a2 |
81225.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81225.2 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{20} \cdot 5^{4} \cdot 19^{2} \) |
$3.01711$ |
$(-a-2), (2a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.134827177$ |
$0.788766240$ |
2.126942524 |
\( \frac{48587168449}{28048275} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -76\) , \( 19\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-76{x}+19$ |
| 4275.2-a2 |
4275.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
4275.2 |
\( 3^{2} \cdot 5^{2} \cdot 19 \) |
\( 3^{20} \cdot 5^{4} \cdot 19^{2} \) |
$3.14956$ |
$(-a), (a-1), (-2a+1), (3)$ |
$3$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.097262643$ |
$0.788766240$ |
5.632063733 |
\( \frac{48587168449}{28048275} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -76\) , \( -19\bigr] \) |
${y}^2+{x}{y}={x}^3-76{x}-19$ |
| 855.2-a2 |
855.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
855.2 |
\( 3^{2} \cdot 5 \cdot 19 \) |
\( 3^{20} \cdot 5^{4} \cdot 19^{2} \) |
$4.70969$ |
$(3,a), (3,a+2), (5,a+2), (19,a+9)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$0.079413606$ |
$0.788766240$ |
5.141281924 |
\( \frac{48587168449}{28048275} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -76\) , \( -19\bigr] \) |
${y}^2+{x}{y}={x}^3-76{x}-19$ |
*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.
