Cremona's table of elliptic curves

48672 = 2⁵ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	48672bs	Isogeny class
Conductor	48672	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	5404790416896 = 29 · 37 · 136	Discriminant
Eigenvalues	2- 3-  2 -4 -4 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-49179,4196270]	[a1,a2,a3,a4,a6]
Generators	[133:90:1]	Generators of the group modulo torsion
j	7301384/3	j-invariant
L	5.3086911118568	L(r)(E,1)/r!
Ω	0.75030934161849	Real period
R	1.7688341385898	Regulator
r	1	Rank of the group of rational points
S	1.000000000005	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48672r4 97344cj4 16224e2 288c3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672bs4

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	-4	-4	+	6	-4	0	-2	4	2	2	-4	-8	-10	4	6	4	16	6	-4	-12	10	14

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Quadratic twists for elliptic curve 48672bs4

-4	8	-3	13
48672r4	97344cj4	16224e2	288c3

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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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