Cremona's table of elliptic curves

4692 = 2² · 3 · 17 · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 17- 23-	Signs for the Atkin-Lehner involutions
Class	4692f	Isogeny class
Conductor	4692	Conductor
∏ cp	147	Product of Tamagawa factors cp
deg	105840	Modular degree for the optimal curve
Δ	2795211703657757952 = 28 · 37 · 177 · 233	Discriminant
Eigenvalues	2- 3- -2  3  2 -5 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1888229,994814775]	[a1,a2,a3,a4,a6]
Generators	[562:10557:1]	Generators of the group modulo torsion
j	2908358687307694538752/10918795717413117	j-invariant
L	4.2948437881832	L(r)(E,1)/r!
Ω	0.25607078297364	Real period
R	0.11409589204254	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18768o1 75072z1 14076b1 117300c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4692f1

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	3	2	-5	-	-2	-	-7	-10	-5	-2	6	-12	9	0	5	0	-3	4	1	1	-9	7

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Quadratic twists for elliptic curve 4692f1

-4	8	-3	5	17	-23
18768o1	75072z1	14076b1	117300c1	79764b1	107916h1

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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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