Cremona's table of elliptic curves

41664 = 2⁶ · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 31-	Signs for the Atkin-Lehner involutions
Class	41664ci	Isogeny class
Conductor	41664	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	239616	Modular degree for the optimal curve
Δ	453939658002432 = 212 · 312 · 7 · 313	Discriminant
Eigenvalues	2- 3+  0 7+ -2 -2 -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-279993,57109689]	[a1,a2,a3,a4,a6]
Generators	[311:124:1]	Generators of the group modulo torsion
j	592661665007992000/110825111817	j-invariant
L	4.3843646653875	L(r)(E,1)/r!
Ω	0.51173638230628	Real period
R	1.4279372534311	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	41664dx1 20832n1 124992et1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 41664ci1

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

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Quadratic twists for elliptic curve 41664ci1

-4	8	-3
41664dx1	20832n1	124992et1

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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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