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-b4 588.1-b $4$
$4$
\(\Q(\sqrt{33}) \) $2$
$[2, 0]$
588.1
\( 2^{2} \cdot 3 \cdot 7^{2} \)
\( - 2^{25} \cdot 3 \cdot 7^{4} \)
$2.52778$
$(-a-2), (-a+3), (-2a+7), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2^{3} \cdot 5 \)
$1$
$1.580678965$
2.751608890
\( \frac{101522315347710125}{154140672} a + \frac{240839492583960875}{154140672} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 4470 a - 15069\) , \( -44025321 a + 148465765\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4470a-15069\right){x}-44025321a+148465765$
588.1-m4 588.1-m $4$
$4$
\(\Q(\sqrt{33}) \) $2$
$[2, 0]$
588.1
\( 2^{2} \cdot 3 \cdot 7^{2} \)
\( - 2^{25} \cdot 3 \cdot 7^{4} \)
$2.52778$
$(-a-2), (-a+3), (-2a+7), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2^{2} \cdot 5 \)
$1$
$3.161357930$
2.751608890
\( \frac{101522315347710125}{154140672} a + \frac{240839492583960875}{154140672} \)
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -23 a - 66\) , \( 563 a - 1268\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-23a-66\right){x}+563a-1268$
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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.
