Cremona's table of elliptic curves

48672 = 2⁵ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3+ 13-	Signs for the Atkin-Lehner involutions
Class	48672bj	Isogeny class
Conductor	48672	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	79872	Modular degree for the optimal curve
Δ	-18324574916544 = -1 · 26 · 33 · 139	Discriminant
Eigenvalues	2- 3+  2  0  0 13- -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,6591,0]	[a1,a2,a3,a4,a6]
Generators	[7350:110915:216]	Generators of the group modulo torsion
j	1728	j-invariant
L	6.7437268367192	L(r)(E,1)/r!
Ω	0.4115469525707	Real period
R	8.1931439348769	Regulator
r	1	Rank of the group of rational points
S	0.9999999999964	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48672bj1 97344eg2 48672h1 48672i1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672bj1

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	0	0	-	-8	0	0	-4	0	12	10	0	0	4	0	-10	0	0	16	0	0	-10	8

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Quadratic twists for elliptic curve 48672bj1

-4	8	-3	13
48672bj1	97344eg2	48672h1	48672i1

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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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