| 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 |
| 18396.2-e1 |
18396.2-e |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18396.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 73 \) |
\( 2^{6} \cdot 3^{9} \cdot 7^{3} \cdot 73 \) |
$1.80252$ |
$(-2a+1), (-3a+1), (9a-8), (2)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.899085400$ |
2.076348791 |
\( -\frac{91698753975}{50078} a - \frac{2296727574189}{200312} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 52 a + 241\) , \( -1854 a + 1379\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(52a+241\right){x}-1854a+1379$ |
| 128772.2-c1 |
128772.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
128772.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 2^{6} \cdot 3^{3} \cdot 7^{9} \cdot 73 \) |
$2.93194$ |
$(-2a+1), (-3a+1), (9a-8), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{3} \) |
$0.311103122$ |
$0.588589557$ |
3.383033314 |
\( -\frac{91698753975}{50078} a - \frac{2296727574189}{200312} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -543 a - 154\) , \( -6567 a + 1550\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-543a-154\right){x}-6567a+1550$ |
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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.
