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	2	Product of Tamagawa factors cp
deg	1008	Modular degree for the optimal curve
Δ	-69923919 = -1 · 3 · 133 · 1032	Discriminant
Eigenvalues	-1 3-  2 -2  4 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,103,0]	[a1,a2,a3,a4,a6]
Generators	[363:1496:27]	Generators of the group modulo torsion
j	120773549807/69923919	j-invariant
L	3.0134300695753	L(r)(E,1)/r!
Ω	1.160732824545	Real period
R	5.1922888813911	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	64272k1 12051d1 100425b1 52221h1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4017c1

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 4017c1

-4	-3	5	13
64272k1	12051d1	100425b1	52221h1

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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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