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
deg	288	Modular degree for the optimal curve
Δ	-25173395 = -1 · 5 · 132 · 313	Discriminant
Eigenvalues	0  1 5+  2  0 13-  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-31,240]	[a1,a2,a3,a4,a6]
Generators	[6:17:1]	Generators of the group modulo torsion
j	-3402072064/25173395	j-invariant
L	2.9132403183169	L(r)(E,1)/r!
Ω	1.8227361638439	Real period
R	2.3974179939789	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	32240j1 128960o1 18135s1 10075a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2015a1

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 2015a1

-4	8	-3	5	-7	13	-31
32240j1	128960o1	18135s1	10075a1	98735t1	26195f1	62465b1

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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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