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-d6
578.1-d
$8$
$12$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
578.1
\( 2 \cdot 17^{2} \)
\( 2^{6} \cdot 17^{4} \)
$1.23927$
$(a), (-3a-1), (3a-1)$
$1$
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{3} \cdot 3 \)
$0.937230688$
$20.21098874$
2.232378405
\( \frac{8805624625}{2312} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -43\) , \( 105\bigr] \)
${y}^2+{x}{y}={x}^{3}-43{x}+105$
4624.1-c6
4624.1-c
$8$
$12$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
4624.1
\( 2^{4} \cdot 17^{2} \)
\( 2^{18} \cdot 17^{4} \)
$2.08419$
$(a), (-3a-1), (3a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3B
$4$
\( 2^{4} \)
$1$
$1.737574322$
2.457301172
\( \frac{8805624625}{2312} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -172\) , \( -840\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-172{x}-840$
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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.