Elliptic curve search results

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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
39.2-b1	39.2-b	$1$	$1$	\(\Q(\sqrt{157}) \)	$2$	$[2, 0]$	39.2	\( 3 \cdot 13 \)	\( 3^{29} \cdot 13^{3} \)	$2.79804$	$(-a-6), (-2a-11)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 29 \)	$0.555699910$	$2.193832103$	5.643153734	\( \frac{30994677524215436107}{150780939070647951} a - \frac{16201418628140718394}{11598533774665227} \)	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -382 a - 2189\) , \( 170330 a + 981950\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-382a-2189\right){x}+170330a+981950$

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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.