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	6240be	Isogeny class
Conductor	6240	Conductor
∏ cp	150	Product of Tamagawa factors cp
deg	9600	Modular degree for the optimal curve
Δ	-6833548800000 = -1 · 212 · 35 · 55 · 133	Discriminant
Eigenvalues	2- 3- 5- -3  3 13- -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,4675,27723]	[a1,a2,a3,a4,a6]
Generators	[241:3900:1]	Generators of the group modulo torsion
j	2758136205824/1668346875	j-invariant
L	4.818818042609	L(r)(E,1)/r!
Ω	0.45946270747351	Real period
R	0.069919610655769	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	6240i1 12480d1 18720i1 31200b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240be1

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	-	-3	-2	1	-8	-4	-5	-7	-2	4	-11	4	1	0	-5	-2	3	4	7	5

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Quadratic twists for elliptic curve 6240be1

-4	8	-3	5	13
6240i1	12480d1	18720i1	31200b1	81120r1

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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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