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	2240k	Isogeny class
Conductor	2240	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	143360000 = 215 · 54 · 7	Discriminant
Eigenvalues	2+  0 5- 7- -4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-332,-2256]	[a1,a2,a3,a4,a6]
Generators	[-10:8:1]	Generators of the group modulo torsion
j	123505992/4375	j-invariant
L	3.1903786538985	L(r)(E,1)/r!
Ω	1.120881003603	Real period
R	0.71157835748023	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2240e3 1120c2 20160br3 11200b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2240k3

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	-	-	-4	-2	6	4	-8	-6	0	-10	10	-12	0	6	-12	-2	-4	-12	-10	-4	0	18	-10

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Quadratic twists for elliptic curve 2240k3

-4	8	-3	5	-7
2240e3	1120c2	20160br3	11200b3	15680e3

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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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