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	-4605254041208832 = -1 · 211 · 312 · 114 · 172	Discriminant
Eigenvalues	2- 3+  2 -4 11+  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17072,3381708]	[a1,a2,a3,a4,a6]
Generators	[213:3060:1]	Generators of the group modulo torsion
j	-268702931670626/2248659199809	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	8976k4 35904bn3 13464j4 112200v3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4488f4

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 4488f4

-4	8	-3	5	-11	17
8976k4	35904bn3	13464j4	112200v3	49368f3	76296v3

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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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