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
4225.1-CMb1
4225.1-CMb
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
4225.1
\( 5^{2} \cdot 13^{2} \)
\( 5^{9} \cdot 13^{6} \)
$1.44087$
$(-a-2), (-3a-2)$
0
$\Z/2\Z$
$\textsf{yes}$
$-4$
$\mathrm{U}(1)$
✓
✓
$5$
5Cs.4.1
$1$
\( 2^{2} \)
$1$
$1.140552436$
1.140552436
\( 1728 \)
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 35 i - 9\) , \( -4 i - 18\bigr] \)
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(35i-9\right){x}-4i-18$
4225.1-CMa1
4225.1-CMa
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
4225.1
\( 5^{2} \cdot 13^{2} \)
\( 5^{6} \cdot 13^{3} \)
$1.44087$
$(-a-2), (-3a-2)$
0
$\Z/2\Z$
$\textsf{yes}$
$-4$
$\mathrm{U}(1)$
✓
✓
$13$
13Cs.4.1
$1$
\( 2^{2} \)
$1$
$3.238497722$
3.238497722
\( 1728 \)
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( i + 3\) , \( 2 i - 1\bigr] \)
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(i+3\right){x}+2i-1$
4225.1-a1
4225.1-a
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
4225.1
\( 5^{2} \cdot 13^{2} \)
\( 5^{3} \cdot 13^{9} \)
$1.44087$
$(-a-2), (-3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3Cn
$1$
\( 2^{2} \)
$1$
$1.351228544$
1.351228544
\( -\frac{906876}{2197} a + \frac{1118799}{2197} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 16 i - 10\) , \( -28 i - 35\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(16i-10\right){x}-28i-35$
4225.1-a2
4225.1-a
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
4225.1
\( 5^{2} \cdot 13^{2} \)
\( 5^{3} \cdot 13^{12} \)
$1.44087$
$(-a-2), (-3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3Cn
$1$
\( 2^{3} \)
$1$
$0.675614272$
1.351228544
\( \frac{10047446145}{4826809} a + \frac{17756992962}{4826809} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -79 i + 100\) , \( -279 i - 367\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-79i+100\right){x}-279i-367$
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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.