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	6240ba	Isogeny class
Conductor	6240	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	798720 = 212 · 3 · 5 · 13	Discriminant
Eigenvalues	2- 3- 5+  0  0 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1041,-13281]	[a1,a2,a3,a4,a6]
Generators	[298:255:8]	Generators of the group modulo torsion
j	30488290624/195	j-invariant
L	4.5513263044284	L(r)(E,1)/r!
Ω	0.84043141678658	Real period
R	5.4154642645685	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	6240a3 12480o1 18720n3 31200d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240ba2

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 6240ba2

-4	8	-3	5	13
6240a3	12480o1	18720n3	31200d4	81120u4

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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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