Cremona's table of elliptic curves

10816 = 2⁶ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	10816r	Isogeny class
Conductor	10816	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	29246464 = 210 · 134	Discriminant
Eigenvalues	2+ -3 -2  1  5 13+  3  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-676,6760]	[a1,a2,a3,a4,a6]
Generators	[13:13:1]	Generators of the group modulo torsion
j	1168128	j-invariant
L	2.6079163947997	L(r)(E,1)/r!
Ω	2.081902134441	Real period
R	0.41755347216004	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	10816bj1 676d1 97344bs1 10816q1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 10816r1

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
+	-3	-2	1	5	+	3	3	-1	1	-8	-3	3	-1	4	6	-5	5	-7	-11	14	-4	-12	-9	-1

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Quadratic twists for elliptic curve 10816r1

-4	8	-3	13
10816bj1	676d1	97344bs1	10816q1

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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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