Cremona's table of elliptic curves

664 = 2³ · 83

Field	Data	Notes
Atkin-Lehner	2- 83+	Signs for the Atkin-Lehner involutions
Class	664a	Isogeny class
Conductor	664	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-21248 = -1 · 28 · 83	Discriminant
Eigenvalues	2- -3 -4 -5 -3 -4 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7,10]	[a1,a2,a3,a4,a6]
Generators	[5:-10:1] [-2:4:1]	Generators of the group modulo torsion
j	-148176/83	j-invariant
L	1.3742026761348	L(r)(E,1)/r!
Ω	3.5536274746825	Real period
R	0.096676050453051	Regulator
r	2	Rank of the group of rational points
S	0.99999999999985	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1328c1 5312g1 5976e1 16600h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 664a1

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
-	-3	-4	-5	-3	-4	-3	-4	0	5	-5	-3	-2	-4	-2	-6	7	-15	-6	-6	-10	-8	+	-12	16

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Quadratic twists for elliptic curve 664a1

-4	8	-3	5	-7	-11	13	-83
1328c1	5312g1	5976e1	16600h1	32536h1	80344d1	112216d1	55112d1

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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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