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	8	Product of Tamagawa factors cp
Δ	3717120 = 211 · 3 · 5 · 112	Discriminant
Eigenvalues	2+ 3+ 5-  0 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-77440,8320480]	[a1,a2,a3,a4,a6]
Generators	[602:13398:1]	Generators of the group modulo torsion
j	25078144523224322/1815	j-invariant
L	2.9680177178993	L(r)(E,1)/r!
Ω	1.3781699542991	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	1320m5 10560ca5 7920c5 13200u5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640f5

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 2640f5

-4	8	-3	5	-7	-11
1320m5	10560ca5	7920c5	13200u5	129360ca6	29040n6

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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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