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	4692a	Isogeny class
Conductor	4692	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-12867040512 = -1 · 28 · 35 · 17 · 233	Discriminant
Eigenvalues	2- 3+  2 -2 -3 -3 17+  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,28,5448]	[a1,a2,a3,a4,a6]
Generators	[-14:46:1]	Generators of the group modulo torsion
j	9148592/50261877	j-invariant
L	3.30896665934	L(r)(E,1)/r!
Ω	0.99334849966491	Real period
R	0.37012484769737	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	18768u1 75072bl1 14076f1 117300bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4692a1

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	-2	-3	-3	+	7	-	-1	9	2	-1	-4	13	-11	3	5	-9	-12	-16	-2	0	-11	-3

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Quadratic twists for elliptic curve 4692a1

-4	8	-3	5	17	-23
18768u1	75072bl1	14076f1	117300bb1	79764h1	107916e1

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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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