Cremona's table of elliptic curves

10816 = 2⁶ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	10816k	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	[-5:18:1]	Generators of the group modulo torsion
j	-10816	j-invariant
L	6.2232956551259	L(r)(E,1)/r!
Ω	2.5807087809234	Real period
R	2.4114676173958	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	10816o1 5408d1 97344bb1 10816j1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 10816k1

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 10816k1

-4	8	-3	13
10816o1	5408d1	97344bb1	10816j1

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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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