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	2240c	Isogeny class
Conductor	2240	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-14336000 = -1 · 214 · 53 · 7	Discriminant
Eigenvalues	2+ -1 5+ 7- -3  1 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-21,-179]	[a1,a2,a3,a4,a6]
j	-65536/875	j-invariant
L	0.95056473647073	L(r)(E,1)/r!
Ω	0.95056473647073	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2240p1 140a1 20160cj1 11200d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2240c1

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
+	-1	+	-	-3	1	-3	-2	-6	9	8	10	0	-2	-3	0	-12	-8	-8	0	14	5	12	12	17

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Quadratic twists for elliptic curve 2240c1

-4	8	-3	5	-7
2240p1	140a1	20160cj1	11200d1	15680bo1

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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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