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	6240r	Isogeny class
Conductor	6240	Conductor
∏ cp	384	Product of Tamagawa factors cp
Δ	-197121600000000 = -1 · 212 · 36 · 58 · 132	Discriminant
Eigenvalues	2+ 3- 5- -2 -2 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6945,708975]	[a1,a2,a3,a4,a6]
Generators	[135:-1500:1]	Generators of the group modulo torsion
j	-9045718037056/48125390625	j-invariant
L	4.7230299498021	L(r)(E,1)/r!
Ω	0.48955246310696	Real period
R	0.10049633563589	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	6240y2 12480h1 18720bf2 31200bo2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240r2

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
+	-	-	-2	-2	+	-2	-2	8	-6	2	2	-2	0	-6	-10	14	-10	-2	6	2	12	-6	-18	-14

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Quadratic twists for elliptic curve 6240r2

-4	8	-3	5	13
6240y2	12480h1	18720bf2	31200bo2	81120br2

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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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