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-c4
578.1-c
$4$
$6$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
578.1
\( 2 \cdot 17^{2} \)
\( 2^{4} \cdot 17^{6} \)
$2.14648$
$(-a+2), (17)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \cdot 3 \)
$1$
$2.245665415$
1.375183600
\( \frac{120920208625}{19652} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -103\) , \( -411\bigr] \)
${y}^2+{x}{y}={x}^{3}-103{x}-411$
578.1-d4
578.1-d
$4$
$6$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
578.1
\( 2 \cdot 17^{2} \)
\( 2^{4} \cdot 17^{6} \)
$2.14648$
$(-a+2), (17)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1.687887029$
$13.90059457$
1.596429988
\( \frac{120920208625}{19652} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2062 a - 5050\) , \( 79317 a + 194286\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2062a-5050\right){x}+79317a+194286$
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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.