Cremona's table of elliptic curves

116928 = 2⁶ · 3² · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 29+	Signs for the Atkin-Lehner involutions
Class	116928dk	Isogeny class
Conductor	116928	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	147456	Modular degree for the optimal curve
Δ	-1125023219712 = -1 · 218 · 36 · 7 · 292	Discriminant
Eigenvalues	2- 3-  2 7+  4  2 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5484,164432]	[a1,a2,a3,a4,a6]
Generators	[76:432:1]	Generators of the group modulo torsion
j	-95443993/5887	j-invariant
L	8.7508157206252	L(r)(E,1)/r!
Ω	0.85675247506768	Real period
R	2.5534842222864	Regulator
r	1	Rank of the group of rational points
S	1.0000000012187	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	116928cb1 29232bg1 12992be1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 116928dk1

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

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Quadratic twists for elliptic curve 116928dk1

-4	8	-3
116928cb1	29232bg1	12992be1

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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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