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-d1
578.1-d
$8$
$12$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
578.1
\( 2 \cdot 17^{2} \)
\( - 2^{3} \cdot 17^{5} \)
$1.23927$
$(a), (-3a-1), (3a-1)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1.874461377$
$10.10549437$
2.232378405
\( -\frac{1712717194041788375}{334084} a + \frac{605536970972065000}{83521} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( 230 a - 363\) , \( -2390 a + 3513\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(230a-363\right){x}-2390a+3513$
4624.1-c1
4624.1-c
$8$
$12$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
4624.1
\( 2^{4} \cdot 17^{2} \)
\( - 2^{15} \cdot 17^{5} \)
$2.08419$
$(a), (-3a-1), (3a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$16$
\( 2^{2} \)
$1$
$0.434393580$
2.457301172
\( -\frac{1712717194041788375}{334084} a + \frac{605536970972065000}{83521} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( 920 a - 1452\) , \( 19120 a - 28104\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(920a-1452\right){x}+19120a-28104$
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Pari/GP
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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.