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
58482.1-a1	58482.1-a	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	58482.1	\( 2 \cdot 3^{4} \cdot 19^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 19^{2} \)	$2.77923$	$(a+1), (3), (19)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{2} \)	$0.237879944$	$3.855564791$	3.668646161	\( \frac{132651}{76} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 1\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+1$
58482.1-g1	58482.1-g	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	58482.1	\( 2 \cdot 3^{4} \cdot 19^{2} \)	\( 2^{4} \cdot 3^{18} \cdot 19^{2} \)	$2.77923$	$(a+1), (3), (19)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$1.551718204$	$1.285188263$	7.977000101	\( \frac{132651}{76} \)	\( \bigl[i\) , \( 1\) , \( i\) , \( -28\) , \( -1\bigr] \)	${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-28{x}-1$

 

  *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.