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	12635a	Isogeny class
Conductor	12635	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4752	Modular degree for the optimal curve
Δ	-1646605835 = -1 · 5 · 7 · 196	Discriminant
Eigenvalues	0 -1 5+ 7- -3 -5  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-481,-4349]	[a1,a2,a3,a4,a6]
Generators	[218:357:8]	Generators of the group modulo torsion
j	-262144/35	j-invariant
L	2.1527875013804	L(r)(E,1)/r!
Ω	0.50587185081896	Real period
R	2.1277992617056	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	113715bj1 63175d1 88445bn1 35a3	Quadratic twists by: -3 5 -7 -19

Hecke Eigenvalues for elliptic curve 12635a1

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
0	-1	+	-	-3	-5	3	-	-6	-3	4	-2	12	-10	9	-12	0	8	4	0	2	1	12	12	1

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Quadratic twists for elliptic curve 12635a1

-3	5	-7	-19
113715bj1	63175d1	88445bn1	35a3

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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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