Cremona's table of elliptic curves

10816 = 2⁶ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	10816b	Isogeny class
Conductor	10816	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-725849473024 = -1 · 232 · 132	Discriminant
Eigenvalues	2+  0 -1 -4  4 13+  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-24908,-1513616]	[a1,a2,a3,a4,a6]
Generators	[30870:339968:125]	Generators of the group modulo torsion
j	-38575685889/16384	j-invariant
L	3.4480670908101	L(r)(E,1)/r!
Ω	0.19000882854464	Real period
R	4.5367195793222	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	10816z2 338a2 97344bf2 10816a2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 10816b2

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	-1	-4	4	+	3	0	-4	1	-4	3	9	8	8	9	-4	-7	4	8	-11	-4	0	6	-2

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Quadratic twists for elliptic curve 10816b2

-4	8	-3	13
10816z2	338a2	97344bf2	10816a2

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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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