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	48672a	Isogeny class
Conductor	48672	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	-1027585778012352 = -1 · 26 · 39 · 138	Discriminant
Eigenvalues	2+ 3+  2  0  2 13+  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-13689,1660932]	[a1,a2,a3,a4,a6]
Generators	[6916:76895:64]	Generators of the group modulo torsion
j	-46656/169	j-invariant
L	7.2136736195264	L(r)(E,1)/r!
Ω	0.43106647803759	Real period
R	4.1836201531949	Regulator
r	1	Rank of the group of rational points
S	0.99999999999821	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48672bb1 97344o2 48672be1 3744j1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672a1

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	2	+	0	-4	-4	8	-8	-2	6	-4	6	4	6	2	-4	6	2	-16	2	10	2

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Quadratic twists for elliptic curve 48672a1

-4	8	-3	13
48672bb1	97344o2	48672be1	3744j1

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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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