Cremona's table of elliptic curves

4165 = 5 · 7² · 17

Field	Data	Notes
Atkin-Lehner	5- 7- 17+	Signs for the Atkin-Lehner involutions
Class	4165l	Isogeny class
Conductor	4165	Conductor
∏ cp	44	Product of Tamagawa factors cp
deg	82368	Modular degree for the optimal curve
Δ	-33496646435546875 = -1 · 511 · 79 · 17	Discriminant
Eigenvalues	-2 -2 5- 7-  2  1 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-489820,-132404926]	[a1,a2,a3,a4,a6]
Generators	[1031:21437:1]	Generators of the group modulo torsion
j	-110470393399988224/284716796875	j-invariant
L	1.3992495192203	L(r)(E,1)/r!
Ω	0.090218023257894	Real period
R	0.35249193330162	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	66640ce1 37485bg1 20825u1 595a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4165l1

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	-	-	2	1	+	-6	9	6	-5	-7	5	-8	-9	2	-14	-13	2	-8	8	16	-1	6	16

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Quadratic twists for elliptic curve 4165l1

-4	-3	5	-7	17
66640ce1	37485bg1	20825u1	595a1	70805r1

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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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