Cremona's table of elliptic curves

2240 = 2⁶ · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	2240v	Isogeny class
Conductor	2240	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-2240 = -1 · 26 · 5 · 7	Discriminant
Eigenvalues	2- -3 5+ 7- -3 -1 -1  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2,-2]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	13824/35	j-invariant
L	1.8016317892563	L(r)(E,1)/r!
Ω	2.3820051396353	Real period
R	0.7563509243864	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2240r1 1120p1 20160fe1 11200ce1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2240v1

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
-	-3	+	-	-3	-1	-1	4	-4	9	-6	8	6	-8	7	8	4	-10	-8	12	-14	5	-16	-14	-17

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Quadratic twists for elliptic curve 2240v1

-4	8	-3	5	-7
2240r1	1120p1	20160fe1	11200ce1	15680dv1

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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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