Cremona's table of elliptic curves

4416 = 2⁶ · 3 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 23-	Signs for the Atkin-Lehner involutions
Class	4416v	Isogeny class
Conductor	4416	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-1098842112 = -1 · 216 · 36 · 23	Discriminant
Eigenvalues	2- 3+  2 -2 -2  2 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-257,2337]	[a1,a2,a3,a4,a6]
Generators	[8:27:1]	Generators of the group modulo torsion
j	-28756228/16767	j-invariant
L	3.345173518491	L(r)(E,1)/r!
Ω	1.4364643081395	Real period
R	1.1643775273552	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	4416g1 1104e1 13248bg1 110400hu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4416v1

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	-2	-2	2	-4	0	-	10	0	4	-6	-4	-8	6	4	-8	-4	-8	6	-6	-6	-4	10

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Quadratic twists for elliptic curve 4416v1

-4	8	-3	5	-23
4416g1	1104e1	13248bg1	110400hu1	101568cr1

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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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