Cremona's table of elliptic curves

2015 = 5 · 13 · 31

Field	Data	Notes
Atkin-Lehner	5+ 13- 31-	Signs for the Atkin-Lehner involutions
Class	2015a	Isogeny class
Conductor	2015	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-18703884875 = -1 · 53 · 136 · 31	Discriminant
Eigenvalues	0  1 5+  2  0 13-  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,279,-6239]	[a1,a2,a3,a4,a6]
Generators	[55:422:1]	Generators of the group modulo torsion
j	2393198821376/18703884875	j-invariant
L	2.9132403183169	L(r)(E,1)/r!
Ω	0.6075787212813	Real period
R	0.79913933132628	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	32240j2 128960o2 18135s2 10075a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2015a2

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	+	2	0	-	3	-7	0	0	-	-7	-9	11	0	3	-15	-10	2	-9	-1	-16	9	6	8

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Quadratic twists for elliptic curve 2015a2

-4	8	-3	5	-7	13	-31
32240j2	128960o2	18135s2	10075a2	98735t2	26195f2	62465b2

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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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