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	2015b	Isogeny class
Conductor	2015	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-1064171875 = -1 · 56 · 133 · 31	Discriminant
Eigenvalues	0 -2 5+ -4  3 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1201,-16504]	[a1,a2,a3,a4,a6]
Generators	[92:812:1]	Generators of the group modulo torsion
j	-191740693970944/1064171875	j-invariant
L	1.4533869992496	L(r)(E,1)/r!
Ω	0.40533075809886	Real period
R	0.59761358273859	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	32240k2 128960p2 18135t2 10075c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2015b2

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	-2	+	-4	3	-	0	2	6	0	-	-7	0	-4	-12	0	-6	8	8	0	5	14	0	15	-10

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Quadratic twists for elliptic curve 2015b2

-4	8	-3	5	-7	13	-31
32240k2	128960p2	18135t2	10075c2	98735u2	26195h2	62465d2

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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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