Cremona's table of elliptic curves

78016 = 2⁶ · 23 · 53

Field	Data	Notes
Atkin-Lehner	2- 23+ 53+	Signs for the Atkin-Lehner involutions
Class	78016j	Isogeny class
Conductor	78016	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-1248256 = -1 · 210 · 23 · 53	Discriminant
Eigenvalues	2-  0  1 -2  0  1 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-32,88]	[a1,a2,a3,a4,a6]
Generators	[-6:8:1] [-2:12:1]	Generators of the group modulo torsion
j	-3538944/1219	j-invariant
L	10.506561557406	L(r)(E,1)/r!
Ω	2.5708342961643	Real period
R	2.0434147726141	Regulator
r	2	Rank of the group of rational points
S	0.99999999999583	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	78016d1 19504f1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 78016j1

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
-	0	1	-2	0	1	-4	-4	+	-9	-2	-2	6	4	5	+	-3	-11	-11	-14	14	-13	3	4	-4

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Quadratic twists for elliptic curve 78016j1

-4	8
78016d1	19504f1

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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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