Cremona's table of elliptic curves

5329 = 73²

Field	Data	Notes
Atkin-Lehner	73+	Signs for the Atkin-Lehner involutions
Class	5329a	Isogeny class
Conductor	5329	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7992	Modular degree for the optimal curve
Δ	11047398519097 = 737	Discriminant
Eigenvalues	1  0 -2 -2  2  6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-6328,-107829]	[a1,a2,a3,a4,a6]
Generators	[4570400:40543973:32768]	Generators of the group modulo torsion
j	185193/73	j-invariant
L	3.7456395139588	L(r)(E,1)/r!
Ω	0.55367975131775	Real period
R	6.7649927689142	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	85264a1 47961d1 73a2	Quadratic twists by: -4 -3 73

Hecke Eigenvalues for elliptic curve 5329a1

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

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Quadratic twists for elliptic curve 5329a1

-4	-3	73
85264a1	47961d1	73a2

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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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