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	4	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	31285510865 = 5 · 7 · 197	Discriminant
Eigenvalues	-1  0 5- 7+ -4  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5122,142104]	[a1,a2,a3,a4,a6]
Generators	[108628:140096:2197]	Generators of the group modulo torsion
j	315821241/665	j-invariant
L	2.5017706686809	L(r)(E,1)/r!
Ω	1.1740179084296	Real period
R	8.5237904829832	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	113715m1 63175n1 88445p1 665b1	Quadratic twists by: -3 5 -7 -19

Hecke Eigenvalues for elliptic curve 12635c1

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 12635c1

-3	5	-7	-19
113715m1	63175n1	88445p1	665b1

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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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