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-c1
578.1-c
$4$
$6$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
578.1
\( 2 \cdot 17^{2} \)
\( 2^{12} \cdot 17^{2} \)
$2.14648$
$(-a+2), (17)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3 \)
$1$
$20.21098874$
1.375183600
\( \frac{3048625}{1088} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( 1\bigr] \)
${y}^2+{x}{y}={x}^{3}-3{x}+1$
578.1-d1
578.1-d
$4$
$6$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
578.1
\( 2 \cdot 17^{2} \)
\( 2^{12} \cdot 17^{2} \)
$2.14648$
$(-a+2), (17)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$0.562629009$
$13.90059457$
1.596429988
\( \frac{3048625}{1088} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 60 a - 150\) , \( 258 a - 634\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(60a-150\right){x}+258a-634$
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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.