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
51.2-a2
51.2-a
$6$
$8$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
51.2
\( 3 \cdot 17 \)
\( 3^{16} \cdot 17^{4} \)
$1.54873$
$(-a^2+1), (2a^2-a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$11.81161603$
0.656200891
\( \frac{257154008212105}{60886809} a^{2} + \frac{479060149170145}{60886809} a + \frac{139274003304361}{60886809} \)
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( 85 a^{2} - 49 a - 279\) , \( 599 a^{2} - 256 a - 1795\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(85a^{2}-49a-279\right){x}+599a^{2}-256a-1795$
153.1-b3
153.1-b
$6$
$8$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.1
\( 3^{2} \cdot 17 \)
\( 3^{22} \cdot 17^{4} \)
$1.85993$
$(-a^2+1), (2a^2-a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$17.44502313$
0.969167952
\( \frac{257154008212105}{60886809} a^{2} + \frac{479060149170145}{60886809} a + \frac{139274003304361}{60886809} \)
\( \bigl[a\) , \( -a\) , \( a^{2} + a - 1\) , \( -24 a^{2} - 25 a - 61\) , \( a^{2} + 407 a + 289\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}-a{x}^{2}+\left(-24a^{2}-25a-61\right){x}+a^{2}+407a+289$
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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.