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
deg	360	Modular degree for the optimal curve
Δ	-9682075 = -1 · 52 · 13 · 313	Discriminant
Eigenvalues	0 -2 5+ -4  3 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,39,-105]	[a1,a2,a3,a4,a6]
Generators	[9:32:1]	Generators of the group modulo torsion
j	6393430016/9682075	j-invariant
L	1.4533869992496	L(r)(E,1)/r!
Ω	1.2159922742966	Real period
R	1.7928407482158	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	32240k1 128960p1 18135t1 10075c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2015b1

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 2015b1

-4	8	-3	5	-7	13	-31
32240k1	128960p1	18135t1	10075c1	98735u1	26195h1	62465d1

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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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