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
10404.5-d3
10404.5-d
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
10404.5
\( 2^{2} \cdot 3^{2} \cdot 17^{2} \)
\( 2^{4} \cdot 3^{6} \cdot 17^{6} \)
$2.55261$
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$1.522098751$
2.152572697
\( \frac{4501995680}{6765201} a + \frac{3926605616}{6765201} \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 2 a + 17\) , \( 15 a - 39\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+17\right){x}+15a-39$
41616.5-p3
41616.5-p
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
41616.5
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \)
\( 2^{4} \cdot 3^{6} \cdot 17^{6} \)
$3.60993$
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$2.413794733$
$1.522098751$
5.195868640
\( \frac{4501995680}{6765201} a + \frac{3926605616}{6765201} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4 a + 18\) , \( -18 a + 23\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a+18\right){x}-18a+23$
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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.