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
400.1-a4
400.1-a
$4$
$6$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
400.1
\( 2^{4} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{6} \)
$2.29568$
$(-a-2), (-a+3), (5)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3^{3} \)
$0.485506214$
$20.68730941$
2.622606252
\( \frac{488095744}{125} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 15211 a - 51292\) , \( -1718199 a + 5794249\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(15211a-51292\right){x}-1718199a+5794249$
400.1-c4
400.1-c
$4$
$6$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
400.1
\( 2^{4} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{6} \)
$2.29568$
$(-a-2), (-a+3), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 3 \)
$2.488649399$
$3.545375530$
2.303882094
\( \frac{488095744}{125} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)
${y}^2={x}^{3}+{x}^{2}-41{x}-116$
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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.