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	16	Product of Tamagawa factors cp
Δ	-124806800313 = -1 · 32 · 138 · 17	Discriminant
Eigenvalues	-1 3+ -2  0  4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,221,17042]	[a1,a2,a3,a4,a6]
Generators	[-20:81:1]	Generators of the group modulo torsion
j	1193377118543/124806800313	j-invariant
L	1.1920969617698	L(r)(E,1)/r!
Ω	0.80119102502653	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	10608ba4 42432s3 1989e4 16575f4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 663b4

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 663b4

-4	8	-3	5	-7	-11	13	17
10608ba4	42432s3	1989e4	16575f4	32487l3	80223c3	8619b4	11271h4

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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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