Cremona's table of elliptic curves

4017 = 3 · 13 · 103

Field	Data	Notes
Atkin-Lehner	3- 13+ 103-	Signs for the Atkin-Lehner involutions
Class	4017c	Isogeny class
Conductor	4017	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	4474451943 = 32 · 136 · 103	Discriminant
Eigenvalues	-1 3-  2 -2  4 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-412,-103]	[a1,a2,a3,a4,a6]
Generators	[-7:53:1]	Generators of the group modulo torsion
j	7735372650433/4474451943	j-invariant
L	3.0134300695753	L(r)(E,1)/r!
Ω	1.160732824545	Real period
R	2.5961444406955	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	64272k2 12051d2 100425b2 52221h2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4017c2

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
-1	-	2	-2	4	+	-6	-2	-2	-2	8	-4	-10	4	-8	4	-8	-2	-4	-8	0	0	4	6	2

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Quadratic twists for elliptic curve 4017c2

-4	-3	5	13
64272k2	12051d2	100425b2	52221h2

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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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