Cremona's table of elliptic curves

10816 = 2⁶ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	10816h	Isogeny class
Conductor	10816	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	9984	Modular degree for the optimal curve
Δ	835308258304 = 210 · 138	Discriminant
Eigenvalues	2+ -1 -2 -1 -1 13+  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2929,43289]	[a1,a2,a3,a4,a6]
Generators	[-56:169:1]	Generators of the group modulo torsion
j	3328	j-invariant
L	2.6034640419401	L(r)(E,1)/r!
Ω	0.82694972680585	Real period
R	1.0494245528871	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	10816be1 1352c1 97344bt1 10816g1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 10816h1

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
+	-1	-2	-1	-1	+	3	-7	1	-3	8	1	11	-11	12	6	9	9	3	-5	-2	-12	4	-1	-1

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Quadratic twists for elliptic curve 10816h1

-4	8	-3	13
10816be1	1352c1	97344bt1	10816g1

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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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