Cremona's table of elliptic curves

4488 = 2³ · 3 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 17-	Signs for the Atkin-Lehner involutions
Class	4488k	Isogeny class
Conductor	4488	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-4222741248 = -1 · 28 · 36 · 113 · 17	Discriminant
Eigenvalues	2- 3- -2  1 11-  2 17- -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-209,3267]	[a1,a2,a3,a4,a6]
Generators	[-11:66:1]	Generators of the group modulo torsion
j	-3962770432/16495083	j-invariant
L	4.0983027247403	L(r)(E,1)/r!
Ω	1.2070484450536	Real period
R	0.094314145236184	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	8976c1 35904j1 13464f1 112200g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4488k1

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	1	-	2	-	-6	-6	-1	-4	0	-9	4	3	11	-11	2	13	-16	-11	8	8	11	8

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Quadratic twists for elliptic curve 4488k1

-4	8	-3	5	-11	17
8976c1	35904j1	13464f1	112200g1	49368o1	76296l1

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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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