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	32	Product of Tamagawa factors cp
Δ	1568160000 = 28 · 34 · 54 · 112	Discriminant
Eigenvalues	2+ 3+ 5-  0 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-340,1600]	[a1,a2,a3,a4,a6]
Generators	[0:40:1]	Generators of the group modulo torsion
j	17029316176/6125625	j-invariant
L	2.9680177178993	L(r)(E,1)/r!
Ω	1.3781699542991	Real period
R	1.0767967000879	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	1320m2 10560ca2 7920c2 13200u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640f2

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 2640f2

-4	8	-3	5	-7	-11
1320m2	10560ca2	7920c2	13200u2	129360ca2	29040n2

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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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