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	2640i	Isogeny class
Conductor	2640	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	87120 = 24 · 32 · 5 · 112	Discriminant
Eigenvalues	2+ 3- 5+ -2 11- -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11,0]	[a1,a2,a3,a4,a6]
Generators	[4:6:1]	Generators of the group modulo torsion
j	10061824/5445	j-invariant
L	3.4652832434352	L(r)(E,1)/r!
Ω	2.9698093436764	Real period
R	1.1668369388135	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	1320a1 10560bu1 7920o1 13200i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640i1

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
+	-	+	-2	-	-4	0	4	-4	6	8	-10	-6	-6	-12	-10	-4	-14	8	8	-4	0	14	-18	-10

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Quadratic twists for elliptic curve 2640i1

-4	8	-3	5	-7	-11
1320a1	10560bu1	7920o1	13200i1	129360bs1	29040y1

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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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