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	48672bm	Isogeny class
Conductor	48672	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	86016	Modular degree for the optimal curve
Δ	26348353282368 = 26 · 38 · 137	Discriminant
Eigenvalues	2- 3-  0  2  0 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-27885,-1775176]	[a1,a2,a3,a4,a6]
Generators	[221:1690:1]	Generators of the group modulo torsion
j	10648000/117	j-invariant
L	6.5267832117148	L(r)(E,1)/r!
Ω	0.36969640390919	Real period
R	2.2068050779885	Regulator
r	1	Rank of the group of rational points
S	1.0000000000043	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48672bn1 97344em2 16224b1 3744f1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672bm1

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	2	0	+	-2	-2	8	-6	2	6	0	-4	-8	6	-4	2	2	-4	2	-12	12	12	18

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Quadratic twists for elliptic curve 48672bm1

-4	8	-3	13
48672bn1	97344em2	16224b1	3744f1

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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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