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	4416u	Isogeny class
Conductor	4416	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-217055232 = -1 · 220 · 32 · 23	Discriminant
Eigenvalues	2- 3+  2  2 -6  2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-97,-767]	[a1,a2,a3,a4,a6]
Generators	[16:39:1]	Generators of the group modulo torsion
j	-389017/828	j-invariant
L	3.6570835795837	L(r)(E,1)/r!
Ω	0.71240840053714	Real period
R	2.5667044190006	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	4416h1 1104i1 13248bf1 110400hx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4416u1

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	-6	2	0	0	-	-6	-8	0	10	-12	8	-2	-12	-4	-12	0	-10	6	14	0	-6

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Quadratic twists for elliptic curve 4416u1

-4	8	-3	5	-23
4416h1	1104i1	13248bf1	110400hx1	101568ct1

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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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