| 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-b3 |
27075.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
27075.2 |
\( 3 \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{8} \cdot 5^{12} \cdot 19^{4} \) |
$1.98537$ |
$(-2a+1), (-5a+3), (-5a+2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.442581553$ |
1.533147475 |
\( \frac{6189976379881}{456890625} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -382 a + 381\) , \( -2467\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-382a+381\right){x}-2467$ |
| 81225.2-c3 |
81225.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81225.2 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{8} \cdot 5^{12} \cdot 19^{4} \) |
$3.01711$ |
$(-a-2), (2a+1), (3), (19)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.426759964$ |
$0.442581553$ |
6.799539173 |
\( \frac{6189976379881}{456890625} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -382\) , \( 2849\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-382{x}+2849$ |
| 4275.2-c3 |
4275.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
4275.2 |
\( 3^{2} \cdot 5^{2} \cdot 19 \) |
\( 3^{8} \cdot 5^{12} \cdot 19^{4} \) |
$3.14956$ |
$(-a), (a-1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.442581553$ |
3.655266190 |
\( \frac{6189976379881}{456890625} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -382\) , \( -2849\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-382{x}-2849$ |
| 855.2-f4 |
855.2-f |
$6$ |
$8$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
855.2 |
\( 3^{2} \cdot 5 \cdot 19 \) |
\( 3^{8} \cdot 5^{12} \cdot 19^{4} \) |
$4.70969$ |
$(3,a), (3,a+2), (5,a+2), (19,a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.442581553$ |
2.179579647 |
\( \frac{6189976379881}{456890625} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -382\) , \( -2849\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-382{x}-2849$ |
*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.
