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	4692c	Isogeny class
Conductor	4692	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1008	Modular degree for the optimal curve
Δ	2702592 = 28 · 33 · 17 · 23	Discriminant
Eigenvalues	2- 3-  0 -5  4 -1 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-93,-369]	[a1,a2,a3,a4,a6]
Generators	[-6:3:1]	Generators of the group modulo torsion
j	351232000/10557	j-invariant
L	4.0332156149419	L(r)(E,1)/r!
Ω	1.5388238903109	Real period
R	0.87365761179403	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	18768k1 75072a1 14076h1 117300j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4692c1

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	-5	4	-1	+	4	+	-1	4	3	-6	-6	-12	-5	0	5	-8	-5	4	-11	11	-3	3

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Quadratic twists for elliptic curve 4692c1

-4	8	-3	5	17	-23
18768k1	75072a1	14076h1	117300j1	79764d1	107916l1

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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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