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	2640f	Isogeny class
Conductor	2640	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-6585104824320 = -1 · 211 · 3 · 5 · 118	Discriminant
Eigenvalues	2+ 3+ 5-  0 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4240,164320]	[a1,a2,a3,a4,a6]
Generators	[21:290:1]	Generators of the group modulo torsion
j	-4117122162722/3215383215	j-invariant
L	2.9680177178993	L(r)(E,1)/r!
Ω	0.68908497714956	Real period
R	4.3071868003518	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	1320m6 10560ca6 7920c6 13200u6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640f6

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

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Quadratic twists for elliptic curve 2640f6

-4	8	-3	5	-7	-11
1320m6	10560ca6	7920c6	13200u6	129360ca5	29040n5

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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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