Cremona's table of elliptic curves

92736 = 2⁶ · 3² · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 23-	Signs for the Atkin-Lehner involutions
Class	92736ek	Isogeny class
Conductor	92736	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	-11537842176 = -1 · 215 · 37 · 7 · 23	Discriminant
Eigenvalues	2- 3-  1 7+ -4  1 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12,5168]	[a1,a2,a3,a4,a6]
Generators	[-11:63:1] [-2:72:1]	Generators of the group modulo torsion
j	-8/483	j-invariant
L	11.349954472826	L(r)(E,1)/r!
Ω	1.0158330931132	Real period
R	0.69831565773272	Regulator
r	2	Rank of the group of rational points
S	0.99999999998254	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	92736ew1 46368o1 30912bg1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 92736ek1

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
-	-	1	+	-4	1	-8	0	-	-9	-2	-11	1	1	-9	4	-14	10	12	-2	4	4	-4	2	7

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Quadratic twists for elliptic curve 92736ek1

-4	8	-3
92736ew1	46368o1	30912bg1

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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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