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	4488f	Isogeny class
Conductor	4488	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	4243046318032896 = 211 · 33 · 11 · 178	Discriminant
Eigenvalues	2- 3+  2 -4 11+  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-40512,182700]	[a1,a2,a3,a4,a6]
Generators	[15908:148835:64]	Generators of the group modulo torsion
j	3590504967602306/2071799959977	j-invariant
L	3.2197464632272	L(r)(E,1)/r!
Ω	0.37234292731564	Real period
R	4.3236304855306	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	8976k3 35904bn4 13464j3 112200v4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4488f3

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	-4	+	2	-	4	-4	6	-8	-2	-6	4	4	2	-4	10	12	-4	-14	-4	-4	-6	2

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Quadratic twists for elliptic curve 4488f3

-4	8	-3	5	-11	17
8976k3	35904bn4	13464j3	112200v4	49368f4	76296v4

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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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