Cremona's table of elliptic curves

2016 = 2⁵ · 3² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+	Signs for the Atkin-Lehner involutions
Class	2016a	Isogeny class
Conductor	2016	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-3024568512 = -1 · 26 · 39 · 74	Discriminant
Eigenvalues	2+ 3+  0 7+ -4  2  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-405,4104]	[a1,a2,a3,a4,a6]
Generators	[3:54:1]	Generators of the group modulo torsion
j	-5832000/2401	j-invariant
L	2.9424131544056	L(r)(E,1)/r!
Ω	1.3353212138532	Real period
R	1.1017623040358	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2016b1 4032r2 2016i1 50400cn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2016a1

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	+	-4	2	4	0	-4	-4	8	-2	-4	-8	-8	4	-8	-2	-8	-12	6	8	-16	-12	-2

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Quadratic twists for elliptic curve 2016a1

-4	8	-3	5	-7
2016b1	4032r2	2016i1	50400cn1	14112d1

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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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