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
121.1-a2 121.1-a $3$
$25$
\(\Q(\sqrt{69}) \) $2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{10} \)
$2.46184$
$(a+2), (a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$5$
5Cs.4.1 $1$
\( 1 \)
$1$
$8.512583687$
1.024794649
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 775 a - 3606\) , \( -43609 a + 202926\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+\left(775a-3606\right){x}-43609a+202926$
121.1-b2 121.1-b $3$
$25$
\(\Q(\sqrt{69}) \) $2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{10} \)
$2.46184$
$(a+2), (a-3)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$5$
5Cs.1.1 $9$
\( 5^{2} \)
$1$
$1.610892258$
1.745357748
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
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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.
