Cremona's table of elliptic curves

6405 = 3 · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 61-	Signs for the Atkin-Lehner involutions
Class	6405j	Isogeny class
Conductor	6405	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-22439608362675 = -1 · 33 · 52 · 74 · 614	Discriminant
Eigenvalues	1 3- 5+ 7+  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-199,227897]	[a1,a2,a3,a4,a6]
Generators	[-47:389:1]	Generators of the group modulo torsion
j	-865250742889/22439608362675	j-invariant
L	5.3420520789847	L(r)(E,1)/r!
Ω	0.54116130100446	Real period
R	0.82262165782322	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	102480bg3 19215r4 32025j3 44835k3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6405j4

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
1	-	+	+	4	-2	2	-4	8	-6	-8	-2	6	-12	8	2	0	-	-12	0	-6	-8	-12	2	2

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Quadratic twists for elliptic curve 6405j4

-4	-3	5	-7
102480bg3	19215r4	32025j3	44835k3

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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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