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	48672cc	Isogeny class
Conductor	48672	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	102503232 = 26 · 36 · 133	Discriminant
Eigenvalues	2- 3- -4  0  0 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-117,0]	[a1,a2,a3,a4,a6]
Generators	[-9:18:1] [-3:18:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	7.7457599778861	L(r)(E,1)/r!
Ω	1.5945045045072	Real period
R	1.2144462364312	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48672cc1 97344gp2 5408e1 48672ba1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672cc1

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
-	-	-4	0	0	-	-2	0	0	-10	0	-12	-8	0	0	-14	0	-10	0	0	16	0	0	-16	8

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Quadratic twists for elliptic curve 48672cc1

-4	8	-3	13
48672cc1	97344gp2	5408e1	48672ba1

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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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