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
578.1-a2
578.1-a
$4$
$6$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
578.1
\( 2 \cdot 17^{2} \)
\( 2^{2} \cdot 17^{12} \)
$2.31846$
$(a+3), (17)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \cdot 3 \)
$0.703601975$
$2.245665415$
3.583227075
\( \frac{159661140625}{48275138} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -113\) , \( -329\bigr] \)
${y}^2+{x}{y}={x}^{3}-113{x}-329$
578.1-b2
578.1-b
$4$
$6$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
578.1
\( 2 \cdot 17^{2} \)
\( 2^{2} \cdot 17^{12} \)
$2.31846$
$(a+3), (17)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$4$
\( 2^{2} \cdot 3 \)
$1$
$3.475148644$
7.880896357
\( \frac{159661140625}{48275138} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -114\) , \( 215\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-114{x}+215$
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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.