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	8	Product of Tamagawa factors cp
Δ	-117577950953472 = -1 · 230 · 32 · 233	Discriminant
Eigenvalues	2+ 3+  0  2  0 -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,12127,85281]	[a1,a2,a3,a4,a6]
Generators	[287:5208:1]	Generators of the group modulo torsion
j	752329532375/448524288	j-invariant
L	3.3276387135848	L(r)(E,1)/r!
Ω	0.36064843193811	Real period
R	4.6134107608652	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	4416z3 138b3 13248o3 110400dy3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4416a3

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 4416a3

-4	8	-3	5	-23
4416z3	138b3	13248o3	110400dy3	101568e3

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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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