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	4416w	Isogeny class
Conductor	4416	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	44930433024 = 220 · 34 · 232	Discriminant
Eigenvalues	2- 3+ -2  0  0  2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1089,-8991]	[a1,a2,a3,a4,a6]
Generators	[135:1512:1]	Generators of the group modulo torsion
j	545338513/171396	j-invariant
L	2.7550634153009	L(r)(E,1)/r!
Ω	0.85154162026925	Real period
R	3.235383156527	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4416i2 1104h2 13248be2 110400hm2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4416w2

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	0	0	2	2	-8	-	2	8	-2	10	8	-8	-2	-4	-2	8	0	-6	-8	-16	18	10

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Quadratic twists for elliptic curve 4416w2

-4	8	-3	5	-23
4416i2	1104h2	13248be2	110400hm2	101568ce2

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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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