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	4488c	Isogeny class
Conductor	4488	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-1120635648 = -1 · 28 · 34 · 11 · 173	Discriminant
Eigenvalues	2+ 3+ -4 -3 11- -4 17-  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,135,-1539]	[a1,a2,a3,a4,a6]
Generators	[45:-306:1]	Generators of the group modulo torsion
j	1055028224/4377483	j-invariant
L	1.9875096210522	L(r)(E,1)/r!
Ω	0.78308834130206	Real period
R	0.10575167131141	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	8976i1 35904bh1 13464o1 112200cl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4488c1

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
+	+	-4	-3	-	-4	-	6	-2	5	0	2	9	-2	-7	9	3	-10	13	6	-11	-8	6	-11	-14

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Quadratic twists for elliptic curve 4488c1

-4	8	-3	5	-11	17
8976i1	35904bh1	13464o1	112200cl1	49368w1	76296f1

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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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