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	48672bn	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	[117:338:1]	Generators of the group modulo torsion
j	10648000/117	j-invariant
L	4.8880353999235	L(r)(E,1)/r!
Ω	0.67138110433199	Real period
R	0.91007092848628	Regulator
r	1	Rank of the group of rational points
S	1.0000000000047	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48672bm1 97344ep2 16224i1 3744e1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672bn1

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 48672bn1

-4	8	-3	13
48672bm1	97344ep2	16224i1	3744e1

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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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