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	6240b	Isogeny class
Conductor	6240	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	658045440 = 29 · 32 · 5 · 134	Discriminant
Eigenvalues	2+ 3+ 5+ -4 -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-536,-4440]	[a1,a2,a3,a4,a6]
Generators	[-11:2:1]	Generators of the group modulo torsion
j	33324076232/1285245	j-invariant
L	2.5008457985792	L(r)(E,1)/r!
Ω	0.99442338386852	Real period
R	2.5148702646657	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	6240k3 12480dh3 18720bn3 31200cg3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240b2

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
+	+	+	-4	-4	+	2	4	0	6	0	10	2	4	-4	-6	4	-2	4	8	-2	-16	-4	10	-2

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Quadratic twists for elliptic curve 6240b2

-4	8	-3	5	13
6240k3	12480dh3	18720bn3	31200cg3	81120bl3

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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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