Cremona's table of elliptic curves

2640 = 2⁴ · 3 · 5 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11+	Signs for the Atkin-Lehner involutions
Class	2640r	Isogeny class
Conductor	2640	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	7855027898572800 = 213 · 320 · 52 · 11	Discriminant
Eigenvalues	2- 3- 5+  0 11+  2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-66616,-5083180]	[a1,a2,a3,a4,a6]
Generators	[-178:1080:1]	Generators of the group modulo torsion
j	7981893677157049/1917731420550	j-invariant
L	3.6096736150973	L(r)(E,1)/r!
Ω	0.30235685182386	Real period
R	0.29846137050668	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	330a3 10560bx3 7920bj3 13200bg3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640r3

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
-	-	+	0	+	2	-2	-8	-4	2	-8	-2	6	-8	4	2	-4	-6	12	12	2	0	-4	-6	-14

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Quadratic twists for elliptic curve 2640r3

-4	8	-3	5	-7	-11
330a3	10560bx3	7920bj3	13200bg3	129360ex4	29040cu4

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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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