Elliptic curve search results

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree/signature	Bad \(p\)	$\Q$-curves	Torsion structure	CM
Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image
j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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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
100156.3-a2	100156.3-a	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	100156.3	\( 2^{2} \cdot 7^{3} \cdot 73 \)	\( 2^{4} \cdot 7^{13} \cdot 73 \)	$2.75339$	$(-3a+1), (3a-2), (-9a+1), (2)$	$0$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B[2]	$1$	\( 2 \)	$1$	$0.394815323$	0.911786933	\( -\frac{5216653760445}{100156} a + \frac{1649019465567}{100156} \)	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -1504 a - 248\) , \( -30559 a + 10328\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1504a-248\right){x}-30559a+10328$

 

  *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.