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	48672y	Isogeny class
Conductor	48672	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	314496	Modular degree for the optimal curve
Δ	-3958108181973504 = -1 · 29 · 36 · 139	Discriminant
Eigenvalues	2+ 3-  3  1  4 13- -5 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-138411,-20049822]	[a1,a2,a3,a4,a6]
Generators	[104087350273594877980622:4765040348837498252768492:48099912165860579081]	Generators of the group modulo torsion
j	-74088	j-invariant
L	8.443561895485	L(r)(E,1)/r!
Ω	0.12365969243451	Real period
R	34.140315770059	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	48672ca1 97344dl1 5408l1 48672cb1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672y1

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
+	-	3	1	4	-	-5	-6	6	4	0	-3	-12	-3	7	2	-2	-12	-4	-11	6	-6	10	-6	0

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Quadratic twists for elliptic curve 48672y1

-4	8	-3	13
48672ca1	97344dl1	5408l1	48672cb1

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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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