Cremona's table of elliptic curves

10816 = 2⁶ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	10816n	Isogeny class
Conductor	10816	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	17472	Modular degree for the optimal curve
Δ	-8822943478336 = -1 · 26 · 1310	Discriminant
Eigenvalues	2+ -2  1  0  4 13+  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9520,-388218]	[a1,a2,a3,a4,a6]
Generators	[138986185:3066427168:274625]	Generators of the group modulo torsion
j	-10816	j-invariant
L	3.5297388113316	L(r)(E,1)/r!
Ω	0.24039592200289	Real period
R	14.683022831349	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	10816j1 5408c1 97344bi1 10816o1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 10816n1

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	1	0	4	+	3	-2	2	-5	-2	5	-3	4	-6	-13	12	7	-14	-6	-7	8	4	-14	2

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Quadratic twists for elliptic curve 10816n1

-4	8	-3	13
10816j1	5408c1	97344bi1	10816o1

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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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