Cremona's table of elliptic curves

4015 = 5 · 11 · 73

Field	Data	Notes
Atkin-Lehner	5+ 11- 73-	Signs for the Atkin-Lehner involutions
Class	4015a	Isogeny class
Conductor	4015	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	200	Modular degree for the optimal curve
Δ	-20075 = -1 · 52 · 11 · 73	Discriminant
Eigenvalues	0 -1 5+ -3 11-  1 -3  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1,7]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	-262144/20075	j-invariant
L	1.8850988715116	L(r)(E,1)/r!
Ω	3.1706608281173	Real period
R	0.29727223656258	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	64240m1 36135h1 20075c1 44165a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4015a1

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	+	-3	-	1	-3	6	-7	6	2	2	6	11	-4	-8	-8	10	-9	0	-	14	-9	-6	2

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Quadratic twists for elliptic curve 4015a1

-4	-3	5	-11
64240m1	36135h1	20075c1	44165a1

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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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