Cremona's table of elliptic curves

2635 = 5 · 17 · 31

Field	Data	Notes
Atkin-Lehner	5- 17- 31+	Signs for the Atkin-Lehner involutions
Class	2635d	Isogeny class
Conductor	2635	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-65875 = -1 · 53 · 17 · 31	Discriminant
Eigenvalues	-1 -2 5- -1 -3 -1 17-  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,5,12]	[a1,a2,a3,a4,a6]
Generators	[-1:3:1]	Generators of the group modulo torsion
j	13651919/65875	j-invariant
L	1.3908525832211	L(r)(E,1)/r!
Ω	2.5018043351308	Real period
R	0.18531326420303	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	42160y1 23715e1 13175b1 129115f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2635d1

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	-2	-	-1	-3	-1	-	5	-4	-2	+	-2	0	12	0	9	-3	5	6	12	-8	-1	11	-4	-3

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Quadratic twists for elliptic curve 2635d1

-4	-3	5	-7	17	-31
42160y1	23715e1	13175b1	129115f1	44795c1	81685h1

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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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