Cremona's table of elliptic curves

54720 = 2⁶ · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	54720bg	Isogeny class
Conductor	54720	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	294912	Modular degree for the optimal curve
Δ	-2384231305052160 = -1 · 226 · 39 · 5 · 192	Discriminant
Eigenvalues	2+ 3- 5+  2 -6  0 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-56748,-5709008]	[a1,a2,a3,a4,a6]
Generators	[3128:174420:1]	Generators of the group modulo torsion
j	-105756712489/12476160	j-invariant
L	4.9214404809725	L(r)(E,1)/r!
Ω	0.15364366853742	Real period
R	4.0039401946888	Regulator
r	1	Rank of the group of rational points
S	1.0000000000084	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	54720dq1 1710r1 18240bp1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 54720bg1

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
+	-	+	2	-6	0	-2	-	-4	-8	-8	4	4	6	12	6	-4	-2	8	0	6	8	4	4	12

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Quadratic twists for elliptic curve 54720bg1

-4	8	-3
54720dq1	1710r1	18240bp1

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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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