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
Δ	214587319023035 = 5 · 7 · 1910	Discriminant
Eigenvalues	-1  0 5- 7+ -4  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-70102,-7091614]	[a1,a2,a3,a4,a6]
Generators	[10983:146218:27]	Generators of the group modulo torsion
j	809818183161/4561235	j-invariant
L	2.5017706686809	L(r)(E,1)/r!
Ω	0.29350447710739	Real period
R	8.5237904829832	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	113715m4 63175n4 88445p4 665b3	Quadratic twists by: -3 5 -7 -19

Hecke Eigenvalues for elliptic curve 12635c3

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 12635c3

-3	5	-7	-19
113715m4	63175n4	88445p4	665b3

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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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