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	663c	Isogeny class
Conductor	663	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	232713 = 34 · 132 · 17	Discriminant
Eigenvalues	-1 3-  0 -2 -2 13+ 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-33,-72]	[a1,a2,a3,a4,a6]
Generators	[-3:3:1]	Generators of the group modulo torsion
j	3981876625/232713	j-invariant
L	1.6326154359075	L(r)(E,1)/r!
Ω	1.9988726758582	Real period
R	0.40838404957597	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	10608o1 42432l1 1989a1 16575b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 663c1

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	-	0	-2	-2	+	-	0	-8	-6	6	4	-12	-4	0	-6	0	-2	0	10	-4	12	-4	-10	16

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Quadratic twists for elliptic curve 663c1

-4	8	-3	5	-7	-11	13	17
10608o1	42432l1	1989a1	16575b1	32487g1	80223o1	8619j1	11271a1

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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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