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.