Cremona's table of elliptic curves

10816 = 2⁶ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	10816o	Isogeny class
Conductor	10816	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-1827904 = -1 · 26 · 134	Discriminant
Eigenvalues	2+ -2 -1  0 -4 13+  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-56,-194]	[a1,a2,a3,a4,a6]
Generators	[13:38:1]	Generators of the group modulo torsion
j	-10816	j-invariant
L	2.4924022188517	L(r)(E,1)/r!
Ω	0.86675982319385	Real period
R	2.8755396271918	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	10816k1 5408i1 97344ba1 10816n1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 10816o1

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 10816o1

-4	8	-3	13
10816k1	5408i1	97344ba1	10816n1

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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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