Cremona's table of elliptic curves

6468 = 2² · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	6468k	Isogeny class
Conductor	6468	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	7056	Modular degree for the optimal curve
Δ	-535711427328 = -1 · 28 · 3 · 78 · 112	Discriminant
Eigenvalues	2- 3-  0 7+ 11+  3 -2 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4573,-125665]	[a1,a2,a3,a4,a6]
Generators	[97:594:1]	Generators of the group modulo torsion
j	-7168000/363	j-invariant
L	4.8534224163036	L(r)(E,1)/r!
Ω	0.28942238095848	Real period
R	2.7948900612722	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25872bd1 103488e1 19404k1 6468c1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6468k1

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	+	+	3	-2	-3	-4	6	-5	-5	-4	5	-6	-10	12	-2	-7	-8	-9	11	4	-18	18

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Quadratic twists for elliptic curve 6468k1

-4	8	-3	-7	-11
25872bd1	103488e1	19404k1	6468c1	71148bj1

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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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