Cremona's table of elliptic curves

12635 = 5 · 7 · 19²

Field	Data	Notes
Atkin-Lehner	5- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	12635c	Isogeny class
Conductor	12635	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	20804864725225 = 52 · 72 · 198	Discriminant
Eigenvalues	-1  0 5- 7+ -4  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-6927,34526]	[a1,a2,a3,a4,a6]
Generators	[126:1009:1]	Generators of the group modulo torsion
j	781229961/442225	j-invariant
L	2.5017706686809	L(r)(E,1)/r!
Ω	0.58700895421478	Real period
R	4.2618952414916	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	113715m2 63175n2 88445p2 665b2	Quadratic twists by: -3 5 -7 -19

Hecke Eigenvalues for elliptic curve 12635c2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-1	0	-	+	-4	2	2	-	-8	-6	8	6	-6	4	8	6	12	-2	-4	12	-6	-12	-4	10	-2

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Quadratic twists for elliptic curve 12635c2

-3	5	-7	-19
113715m2	63175n2	88445p2	665b2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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