Cremona's table of elliptic curves

4464 = 2⁴ · 3² · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 31-	Signs for the Atkin-Lehner involutions
Class	4464o	Isogeny class
Conductor	4464	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-4998537216 = -1 · 213 · 39 · 31	Discriminant
Eigenvalues	2- 3+  1  0 -3 -1  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-27,3402]	[a1,a2,a3,a4,a6]
Generators	[-9:54:1]	Generators of the group modulo torsion
j	-27/62	j-invariant
L	3.8689650371217	L(r)(E,1)/r!
Ω	1.0979763876016	Real period
R	0.88093083804223	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	558e1 17856bp1 4464p1 111600cs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4464o1

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
-	+	1	0	-3	-1	3	-1	-2	2	-	-2	0	4	-7	0	6	-9	-3	1	-8	-1	-5	-6	-7

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Quadratic twists for elliptic curve 4464o1

-4	8	-3	5
558e1	17856bp1	4464p1	111600cs1

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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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