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
51.1-a5
51.1-a
$6$
$8$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
51.1
\( 3 \cdot 17 \)
\( 3^{4} \cdot 17 \)
$1.54873$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$188.9858566$
0.656200891
\( \frac{57227017}{153} a^{2} - \frac{97672967}{153} a - \frac{40772771}{153} \)
\( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( -3 a^{2} + 17 a + 7\) , \( 17 a^{2} - 13 a - 7\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-3a^{2}+17a+7\right){x}+17a^{2}-13a-7$
153.3-b6
153.3-b
$6$
$8$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.3
\( 3^{2} \cdot 17 \)
\( 3^{10} \cdot 17 \)
$1.85993$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$17.44502313$
0.969167952
\( \frac{57227017}{153} a^{2} - \frac{97672967}{153} a - \frac{40772771}{153} \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 2\) , \( a + 1\) , \( -3 a^{2} + a + 3\) , \( -3 a^{2} + 1\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-3a^{2}+a+3\right){x}-3a^{2}+1$
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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.