Cremona's table of elliptic curves

63648 = 2⁵ · 3² · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 13- 17+	Signs for the Atkin-Lehner involutions
Class	63648k	Isogeny class
Conductor	63648	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	541202508288 = 29 · 314 · 13 · 17	Discriminant
Eigenvalues	2+ 3-  2  0  4 13- 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-21459,-1209418]	[a1,a2,a3,a4,a6]
Generators	[173210:519869:1000]	Generators of the group modulo torsion
j	2927889364616/1449981	j-invariant
L	8.0134021932682	L(r)(E,1)/r!
Ω	0.39446646967918	Real period
R	10.15726659893	Regulator
r	1	Rank of the group of rational points
S	0.99999999994108	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	63648l4 127296cf4 21216l4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 63648k4

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

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Quadratic twists for elliptic curve 63648k4

-4	8	-3
63648l4	127296cf4	21216l4

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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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