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-a1 51.3-a $6$
$8$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
51.3
\( 3 \cdot 17 \)
\( 3^{32} \cdot 17^{2} \)
$1.54873$
$(-a^2+1), (a^2+a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $4$
\( 2^{2} \)
$1$
$1.476452004$
0.656200891
\( \frac{9072229692338704}{17065161} a^{2} + \frac{51150856611467521}{51195483} a + \frac{14481770636014835}{51195483} \)
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -543 a^{2} - 968 a - 272\) , \( -13153 a^{2} - 24560 a - 6934\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-543a^{2}-968a-272\right){x}-13153a^{2}-24560a-6934$
153.2-b3 153.2-b $6$
$8$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
153.2
\( 3^{2} \cdot 17 \)
\( 3^{38} \cdot 17^{2} \)
$1.85993$
$(-a^2+1), (a^2+a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $1$
\( 2^{3} \)
$1$
$4.361255784$
0.969167952
\( \frac{9072229692338704}{17065161} a^{2} + \frac{51150856611467521}{51195483} a + \frac{14481770636014835}{51195483} \)
\( \bigl[a^{2} + a - 2\) , \( -a^{2} + 1\) , \( a^{2} - 1\) , \( -149 a^{2} - 154 a - 66\) , \( 1826 a^{2} + 1929 a - 183\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(-149a^{2}-154a-66\right){x}+1826a^{2}+1929a-183$
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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.
