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
539.1-a2 539.1-a $3$
$9$
\(\Q(\sqrt{33}) \) $2$
$[2, 0]$
539.1
\( 7^{2} \cdot 11 \)
\( 7^{12} \cdot 11^{6} \)
$2.47339$
$(-4a-9), (7)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3Cs.1.1 $4$
\( 2^{2} \cdot 3^{2} \)
$1$
$0.602881548$
1.679171307
\( -\frac{13278380032}{156590819} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -18155 a - 43065\) , \( -10448199 a - 24786069\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-18155a-43065\right){x}-10448199a-24786069$
539.1-f2 539.1-f $3$
$9$
\(\Q(\sqrt{33}) \) $2$
$[2, 0]$
539.1
\( 7^{2} \cdot 11 \)
\( 7^{12} \cdot 11^{6} \)
$2.47339$
$(-4a-9), (7)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3Cs.1.1 $1$
\( 2^{2} \cdot 3 \)
$2.235348799$
$2.399122391$
2.489484723
\( -\frac{13278380032}{156590819} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -49\) , \( 600\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-49{x}+600$
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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.
