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-a3 1225.1-a $3$
$9$
\(\Q(\sqrt{3}) \) $2$
$[2, 0]$
1225.1
\( 5^{2} \cdot 7^{2} \)
\( 5^{6} \cdot 7^{6} \)
$1.83132$
$(5), (7)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3Cs.1.1 $1$
\( 3^{2} \)
$1$
$4.446757890$
1.283668432
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 9\) , \( 1\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+9{x}+1$
1225.1-b3 1225.1-b $3$
$9$
\(\Q(\sqrt{3}) \) $2$
$[2, 0]$
1225.1
\( 5^{2} \cdot 7^{2} \)
\( 5^{6} \cdot 7^{6} \)
$1.83132$
$(5), (7)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3Cs.1.1 $1$
\( 3^{2} \)
$1$
$4.862220259$
1.403602087
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( -1\) , \( a\) , \( 9\) , \( -2\bigr] \) ${y}^2+a{y}={x}^{3}-{x}^{2}+9{x}-2$
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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.
