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	-1341366278336875 = -1 · 54 · 74 · 197	Discriminant
Eigenvalues	-1  0 5- 7+ -4  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,27368,254014]	[a1,a2,a3,a4,a6]
Generators	[52:1321:1]	Generators of the group modulo torsion
j	48188806119/28511875	j-invariant
L	2.5017706686809	L(r)(E,1)/r!
Ω	0.29350447710739	Real period
R	2.1309476207458	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	113715m3 63175n3 88445p3 665b4	Quadratic twists by: -3 5 -7 -19

Hecke Eigenvalues for elliptic curve 12635c4

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 12635c4

-3	5	-7	-19
113715m3	63175n3	88445p3	665b4

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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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