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	6240a	Isogeny class
Conductor	6240	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-336960000 = -1 · 29 · 34 · 54 · 13	Discriminant
Eigenvalues	2+ 3+ 5+  0  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,64,840]	[a1,a2,a3,a4,a6]
Generators	[29:162:1]	Generators of the group modulo torsion
j	55742968/658125	j-invariant
L	3.1380764817172	L(r)(E,1)/r!
Ω	1.2618541843967	Real period
R	2.4868772640457	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	6240ba4 12480bh4 18720bj4 31200cb2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240a4

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

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Quadratic twists for elliptic curve 6240a4

-4	8	-3	5	13
6240ba4	12480bh4	18720bj4	31200cb2	81120bg2

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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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