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	41664df	Isogeny class
Conductor	41664	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	10240	Modular degree for the optimal curve
Δ	31997952 = 214 · 32 · 7 · 31	Discriminant
Eigenvalues	2- 3-  0 7+ -2  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-273,-1809]	[a1,a2,a3,a4,a6]
Generators	[41:240:1]	Generators of the group modulo torsion
j	137842000/1953	j-invariant
L	7.6052837632463	L(r)(E,1)/r!
Ω	1.1751652943954	Real period
R	3.2358357583908	Regulator
r	1	Rank of the group of rational points
S	0.99999999999968	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	41664y1 10416a1 124992ei1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 41664df1

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	6	2	4	6	-4	+	-2	0	-4	6	0	-6	2	-12	0	-6	-16	-8	-14	-18

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Quadratic twists for elliptic curve 41664df1

-4	8	-3
41664y1	10416a1	124992ei1

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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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