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	2240r	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]
j	13824/35	j-invariant
L	3.2281832622671	L(r)(E,1)/r!
Ω	3.2281832622671	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	2240v1 1120n1 20160es1 11200ct1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2240r1

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 2240r1

-4	8	-3	5	-7
2240v1	1120n1	20160es1	11200ct1	15680dx1

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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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