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	4416a	Isogeny class
Conductor	4416	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	7450890256515072 = 224 · 3 · 236	Discriminant
Eigenvalues	2+ 3+  0  2  0 -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-49313,736545]	[a1,a2,a3,a4,a6]
Generators	[112777:1532392:343]	Generators of the group modulo torsion
j	50591419971625/28422890688	j-invariant
L	3.3276387135848	L(r)(E,1)/r!
Ω	0.36064843193811	Real period
R	9.2268215217303	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	4416z4 138b4 13248o4 110400dy4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4416a4

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

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Quadratic twists for elliptic curve 4416a4

-4	8	-3	5	-23
4416z4	138b4	13248o4	110400dy4	101568e4

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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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