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
1225.2-a1
1225.2-a
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1225.2
\( 5^{2} \cdot 7^{2} \)
\( 5^{18} \cdot 7^{2} \)
$0.91566$
$(-3a+1), (3a-2), (5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1[2]
$1$
\( 3^{2} \)
$1$
$0.774975202$
0.894864283
\( -\frac{250523582464}{13671875} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-131{x}-650$
1225.2-a2
1225.2-a
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1225.2
\( 5^{2} \cdot 7^{2} \)
\( 5^{2} \cdot 7^{2} \)
$0.91566$
$(-3a+1), (3a-2), (5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1[2]
$1$
\( 1 \)
$1$
$6.974776820$
0.894864283
\( -\frac{262144}{35} \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}$
1225.2-a3
1225.2-a
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1225.2
\( 5^{2} \cdot 7^{2} \)
\( 5^{6} \cdot 7^{6} \)
$0.91566$
$(-3a+1), (3a-2), (5)$
0
$\Z/3\Z\oplus\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1[2]
$1$
\( 3^{3} \)
$1$
$2.324925606$
0.894864283
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( 9 a - 9\) , \( 1\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(9a-9\right){x}+1$
1225.2-a4
1225.2-a
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1225.2
\( 5^{2} \cdot 7^{2} \)
\( 5^{2} \cdot 7^{10} \)
$0.91566$
$(-3a+1), (3a-2), (5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 3^{2} \)
$1$
$0.774975202$
0.894864283
\( -\frac{26173471007965184}{201768035} a + \frac{33352919446093824}{201768035} \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( 509 a - 459\) , \( -4730 a + 1976\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(509a-459\right){x}-4730a+1976$
1225.2-a5
1225.2-a
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1225.2
\( 5^{2} \cdot 7^{2} \)
\( 5^{2} \cdot 7^{10} \)
$0.91566$
$(-3a+1), (3a-2), (5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 3^{2} \)
$1$
$0.774975202$
0.894864283
\( \frac{26173471007965184}{201768035} a + \frac{1435889687625728}{40353607} \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( 459 a - 509\) , \( 4730 a - 2754\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(459a-509\right){x}+4730a-2754$
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Pari/GP
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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.