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
588.1-d2 588.1-d $2$
$2$
\(\Q(\sqrt{33}) \) $2$
$[2, 0]$
588.1
\( 2^{2} \cdot 3 \cdot 7^{2} \)
\( - 2^{7} \cdot 3^{2} \cdot 7^{2} \)
$2.52778$
$(-a-2), (-a+3), (-2a+7), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \cdot 5 \)
$1$
$2.783319616$
2.422568772
\( \frac{491441498361}{224} a + \frac{15613894844}{3} \)
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -14 a - 34\) , \( -48 a - 120\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-14a-34\right){x}-48a-120$
588.1-k2 588.1-k $2$
$2$
\(\Q(\sqrt{33}) \) $2$
$[2, 0]$
588.1
\( 2^{2} \cdot 3 \cdot 7^{2} \)
\( - 2^{7} \cdot 3^{2} \cdot 7^{2} \)
$2.52778$
$(-a-2), (-a+3), (-2a+7), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$1$
$19.68882810$
3.427385045
\( \frac{491441498361}{224} a + \frac{15613894844}{3} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 551 a - 1853\) , \( -93367 a + 314857\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(551a-1853\right){x}-93367a+314857$
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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.
