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-a6 51.1-a $6$
$8$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
51.1
\( 3 \cdot 17 \)
\( 3^{32} \cdot 17^{2} \)
$1.54873$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $4$
\( 2^{2} \)
$1$
$1.476452004$
0.656200891
\( \frac{51150856611467521}{51195483} a^{2} - \frac{78367545688483633}{51195483} a - \frac{3709618270320887}{5688387} \)
\( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( -963 a^{2} + 1517 a + 577\) , \( -24013 a^{2} + 36905 a + 15491\bigr] \) ${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-963a^{2}+1517a+577\right){x}-24013a^{2}+36905a+15491$
153.3-b4 153.3-b $6$
$8$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
153.3
\( 3^{2} \cdot 17 \)
\( 3^{38} \cdot 17^{2} \)
$1.85993$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $1$
\( 2^{3} \)
$1$
$4.361255784$
0.969167952
\( \frac{51150856611467521}{51195483} a^{2} - \frac{78367545688483633}{51195483} a - \frac{3709618270320887}{5688387} \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 2\) , \( a + 1\) , \( -153 a^{2} + 301 a - 57\) , \( 1929 a^{2} - 3756 a - 389\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-153a^{2}+301a-57\right){x}+1929a^{2}-3756a-389$
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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.
