Cremona's table of elliptic curves

4046 = 2 · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2- 7+ 17-	Signs for the Atkin-Lehner involutions
Class	4046n	Isogeny class
Conductor	4046	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	19584	Modular degree for the optimal curve
Δ	3200142677573632 = 216 · 7 · 178	Discriminant
Eigenvalues	2- -1  0 7+  4 -2 17- -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-55783,-4302051]	[a1,a2,a3,a4,a6]
Generators	[-169:662:1]	Generators of the group modulo torsion
j	2751936625/458752	j-invariant
L	4.3873846090432	L(r)(E,1)/r!
Ω	0.31417114811799	Real period
R	0.29093647385916	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	32368bj1 129472s1 36414ba1 101150y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4046n1

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	0	+	4	-2	-	-3	4	-5	3	2	-8	-6	-9	5	-5	12	4	6	-14	-6	-5	-12	-6

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Quadratic twists for elliptic curve 4046n1

-4	8	-3	5	-7	17
32368bj1	129472s1	36414ba1	101150y1	28322bf1	4046p1

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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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