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-a4 51.1-a $6$
$8$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
51.1
\( 3 \cdot 17 \)
\( 3^{8} \cdot 17^{2} \)
$1.54873$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{2} \)
$1$
$94.49292831$
0.656200891
\( \frac{21862041663547}{7803} a^{2} + \frac{41087226515522}{7803} a + \frac{3877536454165}{2601} \)
\( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( -3 a^{2} + 17 a + 2\) , \( 11 a^{2} - 8 a - 6\bigr] \) ${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-3a^{2}+17a+2\right){x}+11a^{2}-8a-6$
153.3-b5 153.3-b $6$
$8$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
153.3
\( 3^{2} \cdot 17 \)
\( 3^{14} \cdot 17^{2} \)
$1.85993$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2Cs $1$
\( 2^{3} \)
$1$
$17.44502313$
0.969167952
\( \frac{21862041663547}{7803} a^{2} + \frac{41087226515522}{7803} a + \frac{3877536454165}{2601} \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 2\) , \( a + 1\) , \( -8 a^{2} - 19 a - 17\) , \( -52 a^{2} - 79 a - 3\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-8a^{2}-19a-17\right){x}-52a^{2}-79a-3$
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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.
