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
deg	2304	Modular degree for the optimal curve
Δ	-177209344 = -1 · 220 · 132	Discriminant
Eigenvalues	2+  0 -1 -4  4 13+  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,52,624]	[a1,a2,a3,a4,a6]
Generators	[14:64:1]	Generators of the group modulo torsion
j	351/4	j-invariant
L	3.4480670908101	L(r)(E,1)/r!
Ω	1.3300617998125	Real period
R	0.64810279704603	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	10816z1 338a1 97344bf1 10816a1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 10816b1

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 10816b1

-4	8	-3	13
10816z1	338a1	97344bf1	10816a1

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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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