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
100156.4-c2
100156.4-c
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
100156.4
\( 2^{2} \cdot 7^{3} \cdot 73 \)
\( 2^{2} \cdot 7^{21} \cdot 73^{2} \)
$2.75339$
$(-3a+1), (3a-2), (9a-8), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{3} \)
$3.520772813$
$0.189118281$
3.075394794
\( \frac{637509743623817073}{147520438988258} a - \frac{217278319585716315}{73760219494129} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -777 a - 1015\) , \( 22687 a + 5929\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-777a-1015\right){x}+22687a+5929$
100156.6-d2
100156.6-d
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
100156.6
\( 2^{2} \cdot 7^{3} \cdot 73 \)
\( 2^{2} \cdot 7^{21} \cdot 73^{2} \)
$2.75339$
$(-3a+1), (3a-2), (9a-8), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$4$
\( 2^{3} \)
$1$
$0.189118281$
1.746999853
\( \frac{637509743623817073}{147520438988258} a - \frac{217278319585716315}{73760219494129} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( 287 a + 1393\) , \( 27587 a - 24451\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(287a+1393\right){x}+27587a-24451$
128772.4-g2
128772.4-g
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
128772.4
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 73 \)
\( 2^{2} \cdot 3^{6} \cdot 7^{15} \cdot 73^{2} \)
$2.93194$
$(-2a+1), (-3a+1), (3a-2), (9a-8), (2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1[2]
$1$
\( 2^{5} \cdot 3^{2} \)
$1$
$0.288882946$
2.668586355
\( \frac{637509743623817073}{147520438988258} a - \frac{217278319585716315}{73760219494129} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -168 a + 735\) , \( 8379 a - 3087\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-168a+735\right){x}+8379a-3087$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.