Cremona's table of elliptic curves

663 = 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	3+ 13- 17-	Signs for the Atkin-Lehner involutions
Class	663b	Isogeny class
Conductor	663	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	25857 = 32 · 132 · 17	Discriminant
Eigenvalues	-1 3+ -2  0  4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-539,4592]	[a1,a2,a3,a4,a6]
Generators	[-12:103:1]	Generators of the group modulo torsion
j	17319700013617/25857	j-invariant
L	1.1920969617698	L(r)(E,1)/r!
Ω	3.2047641001061	Real period
R	1.4879060355554	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	10608ba1 42432s1 1989e1 16575f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 663b1

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	0	4	-	-	-4	0	-2	-8	-2	2	-4	8	-10	4	14	-4	0	-14	-8	-4	-6	-6

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Quadratic twists for elliptic curve 663b1

-4	8	-3	5	-7	-11	13	17
10608ba1	42432s1	1989e1	16575f1	32487l1	80223c1	8619b1	11271h1

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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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