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
51.3-a3
51.3-a
$6$
$8$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
51.3
\( 3 \cdot 17 \)
\( 3^{16} \cdot 17^{4} \)
$1.54873$
$(-a^2+1), (a^2+a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$11.81161603$
0.656200891
\( \frac{479060149170145}{60886809} a^{2} - \frac{736214157382250}{60886809} a - \frac{304538278611719}{60886809} \)
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -48 a^{2} - 38 a - 12\) , \( -255 a^{2} - 344 a - 86\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-48a^{2}-38a-12\right){x}-255a^{2}-344a-86$
153.2-b4
153.2-b
$6$
$8$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.2
\( 3^{2} \cdot 17 \)
\( 3^{22} \cdot 17^{4} \)
$1.85993$
$(-a^2+1), (a^2+a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$17.44502313$
0.969167952
\( \frac{479060149170145}{60886809} a^{2} - \frac{736214157382250}{60886809} a - \frac{304538278611719}{60886809} \)
\( \bigl[a^{2} + a - 2\) , \( -a^{2} + 1\) , \( a^{2} - 1\) , \( -24 a^{2} + 46 a - 61\) , \( 408 a^{2} - 410 a - 524\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(-24a^{2}+46a-61\right){x}+408a^{2}-410a-524$
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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.