Cremona's table of elliptic curves

5046 = 2 · 3 · 29²

Field	Data	Notes
Atkin-Lehner	2- 3+ 29-	Signs for the Atkin-Lehner involutions
Class	5046k	Isogeny class
Conductor	5046	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16240	Modular degree for the optimal curve
Δ	-87042875855214 = -1 · 2 · 3 · 299	Discriminant
Eigenvalues	2- 3+ -1  3  0 -4  3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,9654,-257115]	[a1,a2,a3,a4,a6]
Generators	[5721486:78237419:39304]	Generators of the group modulo torsion
j	6859/6	j-invariant
L	4.886331104103	L(r)(E,1)/r!
Ω	0.33308431565542	Real period
R	7.3349762724312	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	40368bo1 15138m1 126150bl1 5046f1	Quadratic twists by: -4 -3 5 29

Hecke Eigenvalues for elliptic curve 5046k1

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	3	0	-4	3	-1	-6	-	-10	-3	-5	1	7	-6	-5	10	2	-12	4	14	4	-6	-8

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Quadratic twists for elliptic curve 5046k1

-4	-3	5	29
40368bo1	15138m1	126150bl1	5046f1

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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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