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-a1 51.1-a $6$
$8$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
51.1
\( 3 \cdot 17 \)
\( - 3^{8} \cdot 17^{8} \)
$1.54873$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{4} \)
$1$
$1.476452004$
0.656200891
\( -\frac{73067274470120883503414977}{188345450907} a^{2} + \frac{25375998117751504521013489}{188345450907} a + \frac{70129610583765315423118325}{62781816969} \)
\( \bigl[a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\) , \( 417 a^{2} - 133 a - 1203\) , \( 4217 a^{2} - 237 a - 14449\bigr] \) ${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(417a^{2}-133a-1203\right){x}+4217a^{2}-237a-14449$
153.3-b1 153.3-b $6$
$8$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
153.3
\( 3^{2} \cdot 17 \)
\( - 3^{14} \cdot 17^{8} \)
$1.85993$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $1$
\( 2^{2} \)
$1$
$8.722511568$
0.969167952
\( -\frac{73067274470120883503414977}{188345450907} a^{2} + \frac{25375998117751504521013489}{188345450907} a + \frac{70129610583765315423118325}{62781816969} \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 2\) , \( a + 1\) , \( 1127 a^{2} - 429 a - 3307\) , \( -24521 a^{2} + 8398 a + 70853\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(1127a^{2}-429a-3307\right){x}-24521a^{2}+8398a+70853$
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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.
