Cremona's table of elliptic curves

6240 = 2⁵ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13+	Signs for the Atkin-Lehner involutions
Class	6240w	Isogeny class
Conductor	6240	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-7188480 = -1 · 212 · 33 · 5 · 13	Discriminant
Eigenvalues	2- 3+ 5- -1 -1 13+ -5  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-125,597]	[a1,a2,a3,a4,a6]
Generators	[7:4:1]	Generators of the group modulo torsion
j	-53157376/1755	j-invariant
L	3.4561554203225	L(r)(E,1)/r!
Ω	2.3441756711837	Real period
R	0.73717927005387	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	6240o1 12480z1 18720f1 31200q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240w1

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	-1	+	-5	2	7	0	4	-7	-11	6	0	11	4	-7	8	-9	2	3	0	3	7

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Quadratic twists for elliptic curve 6240w1

-4	8	-3	5	13
6240o1	12480z1	18720f1	31200q1	81120a1

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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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