Cremona's table of elliptic curves

5015 = 5 · 17 · 59

Field	Data	Notes
Atkin-Lehner	5+ 17- 59-	Signs for the Atkin-Lehner involutions
Class	5015b	Isogeny class
Conductor	5015	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	416	Modular degree for the optimal curve
Δ	-25075 = -1 · 52 · 17 · 59	Discriminant
Eigenvalues	0  0 5+  0 -1  4 17- -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-248,1503]	[a1,a2,a3,a4,a6]
Generators	[9:0:1]	Generators of the group modulo torsion
j	-1686858891264/25075	j-invariant
L	2.7409289836986	L(r)(E,1)/r!
Ω	3.4511525189318	Real period
R	0.39710342684985	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	80240l1 45135l1 25075c1 85255c1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5015b1

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	0	+	0	-1	4	-	-5	1	0	4	6	-4	4	6	7	-	7	-8	-10	-5	-8	4	0	1

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Quadratic twists for elliptic curve 5015b1

-4	-3	5	17
80240l1	45135l1	25075c1	85255c1

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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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