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	4046o	Isogeny class
Conductor	4046	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	3019804928 = 28 · 74 · 173	Discriminant
Eigenvalues	2-  0  0 7-  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-760,7803]	[a1,a2,a3,a4,a6]
Generators	[-21:129:1]	Generators of the group modulo torsion
j	9869198625/614656	j-invariant
L	5.246181697909	L(r)(E,1)/r!
Ω	1.4000048104909	Real period
R	0.23420373534598	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32368g1 129472y1 36414bd1 101150a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4046o1

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	0	-	0	2	+	-4	-8	-8	-8	8	-8	4	-8	10	12	0	-4	8	-8	-8	4	6	-8

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Quadratic twists for elliptic curve 4046o1

-4	8	-3	5	-7	17
32368g1	129472y1	36414bd1	101150a1	28322r1	4046h1

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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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