Cremona's table of elliptic curves

6640 = 2⁴ · 5 · 83

Field	Data	Notes
Atkin-Lehner	2- 5+ 83-	Signs for the Atkin-Lehner involutions
Class	6640d	Isogeny class
Conductor	6640	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-33200 = -1 · 24 · 52 · 83	Discriminant
Eigenvalues	2- -1 5+  1 -3  2  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1381,-19300]	[a1,a2,a3,a4,a6]
Generators	[88:730:1]	Generators of the group modulo torsion
j	-18217937403904/2075	j-invariant
L	3.0445680508279	L(r)(E,1)/r!
Ω	0.39155694647806	Real period
R	3.8877717254321	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1660a1 26560q1 59760bj1 33200s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6640d1

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	+	1	-3	2	3	-2	0	-3	-5	11	6	10	-6	6	-9	5	-8	-12	14	4	-	-6	-16

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Quadratic twists for elliptic curve 6640d1

-4	8	-3	5
1660a1	26560q1	59760bj1	33200s1

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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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