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	2015c	Isogeny class
Conductor	2015	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-654875 = -1 · 53 · 132 · 31	Discriminant
Eigenvalues	-2 -3 5- -4 -6 13+ -1  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-127,552]	[a1,a2,a3,a4,a6]
Generators	[12:-28:1] [-8:32:1]	Generators of the group modulo torsion
j	-226534772736/654875	j-invariant
L	1.3266080246989	L(r)(E,1)/r!
Ω	2.8867679223678	Real period
R	0.076591310211108	Regulator
r	2	Rank of the group of rational points
S	1.0000000000012	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32240m1 128960i1 18135g1 10075d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2015c1

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
-2	-3	-	-4	-6	+	-1	1	-8	6	+	-11	-5	-5	0	-9	-15	-10	4	-1	-9	-10	1	0	-12

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Quadratic twists for elliptic curve 2015c1

-4	8	-3	5	-7	13	-31
32240m1	128960i1	18135g1	10075d1	98735n1	26195e1	62465l1

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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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