Cremona's table of elliptic curves

4732 = 2² · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	4732b	Isogeny class
Conductor	4732	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	20160	Modular degree for the optimal curve
Δ	-269981267256064 = -1 · 28 · 75 · 137	Discriminant
Eigenvalues	2-  0  3 7+  2 13+ -4  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-98696,11960468]	[a1,a2,a3,a4,a6]
j	-86044336128/218491	j-invariant
L	2.20922778105	L(r)(E,1)/r!
Ω	0.55230694526249	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18928v1 75712d1 42588k1 118300n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4732b1

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	3	+	2	+	-4	1	-7	7	5	-4	6	9	7	11	0	-2	10	0	-7	1	11	1	13

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Quadratic twists for elliptic curve 4732b1

-4	8	-3	5	-7	13
18928v1	75712d1	42588k1	118300n1	33124j1	364a1

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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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