| 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 |
| 27900.2-b1 |
27900.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
27900.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 31 \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{20} \cdot 31 \) |
$2.00032$ |
$(-2a+1), (6a-5), (2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.316203733$ |
2.920964966 |
\( \frac{507226797683}{242187500} a + \frac{309491975847}{605468750} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 258 a - 579\) , \( 1203 a - 4041\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(258a-579\right){x}+1203a-4041$ |
| 96100.3-a1 |
96100.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
96100.3 |
\( 2^{2} \cdot 5^{2} \cdot 31^{2} \) |
\( 2^{4} \cdot 5^{20} \cdot 31^{7} \) |
$2.72508$ |
$(6a-5), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1.498448154$ |
$0.098366399$ |
3.403986729 |
\( \frac{507226797683}{242187500} a + \frac{309491975847}{605468750} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 5809 a - 1609\) , \( -101245 a - 36864\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5809a-1609\right){x}-101245a-36864$ |
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*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.
