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	92608836489 = 38 · 132 · 174	Discriminant
Eigenvalues	-1 3+ -2  0  4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1389,-14094]	[a1,a2,a3,a4,a6]
Generators	[-27:81:1]	Generators of the group modulo torsion
j	296380748763217/92608836489	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	10608ba3 42432s4 1989e3 16575f3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 663b3

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 663b3

-4	8	-3	5	-7	-11	13	17
10608ba3	42432s4	1989e3	16575f3	32487l4	80223c4	8619b3	11271h3

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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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