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
722.1-a2 722.1-a $3$
$9$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
722.1
\( 2 \cdot 19^{2} \)
\( 2^{54} \cdot 19^{2} \)
$0.92641$
$(a+1), (19)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3B.1.2 $1$
\( 2 \)
$1$
$0.378954466$
0.757908933
\( -\frac{69173457625}{2550136832} \)
\( \bigl[i\) , \( 0\) , \( i\) , \( -85\) , \( 2456\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}-85{x}+2456$
58482.1-f2 58482.1-f $3$
$9$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
58482.1
\( 2 \cdot 3^{4} \cdot 19^{2} \)
\( 2^{54} \cdot 3^{12} \cdot 19^{2} \)
$2.77923$
$(a+1), (3), (19)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1 $1$
\( 2 \cdot 3^{3} \)
$4.539488286$
$0.126318155$
6.881037449
\( -\frac{69173457625}{2550136832} \)
\( \bigl[i\) , \( 1\) , \( i\) , \( -769\) , \( -66305\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-769{x}-66305$
92416.1-d2 92416.1-d $3$
$9$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
92416.1
\( 2^{8} \cdot 19^{2} \)
\( 2^{78} \cdot 19^{2} \)
$3.11606$
$(a+1), (19)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B $1$
\( 2^{2} \)
$4.253363854$
$0.094738616$
6.447324923
\( -\frac{69173457625}{2550136832} \)
\( \bigl[0\) , \( -i\) , \( 0\) , \( 1368\) , \( -157168 i\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+1368{x}-157168i$
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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.
