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
1225.1-a2
1225.1-a
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
1225.1
\( 5^{2} \cdot 7^{2} \)
\( 5^{2} \cdot 7^{2} \)
$1.49526$
$(5), (7)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 1 \)
$2.271490452$
$6.974776820$
2.489509108
\( -\frac{262144}{35} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-{x}$
19600.1-c2
19600.1-c
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
19600.1
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \)
\( 2^{12} \cdot 5^{2} \cdot 7^{2} \)
$2.99053$
$(a), (5), (7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 1 \)
$0.631888037$
$3.487388410$
3.116416187
\( -\frac{262144}{35} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5\) , \( 7\bigr] \)
${y}^2={x}^{3}-{x}^{2}-5{x}+7$
30625.1-b2
30625.1-b
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
30625.1
\( 5^{4} \cdot 7^{2} \)
\( 5^{14} \cdot 7^{2} \)
$3.34351$
$(5), (7)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2^{2} \)
$0.242252866$
$1.394955364$
3.823263413
\( -\frac{262144}{35} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -33\) , \( 93\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-33{x}+93$
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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.