Cremona's table of elliptic curves

10816 = 2⁶ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13-	Signs for the Atkin-Lehner involutions
Class	10816bo	Isogeny class
Conductor	10816	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	59904	Modular degree for the optimal curve
Δ	-22239247069085696 = -1 · 221 · 139	Discriminant
Eigenvalues	2- -1 -3 -3  0 13- -3  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,32223,6810049]	[a1,a2,a3,a4,a6]
Generators	[-56:2197:1]	Generators of the group modulo torsion
j	1331/8	j-invariant
L	2.035981565333	L(r)(E,1)/r!
Ω	0.27596250824439	Real period
R	1.8444367482067	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	10816t1 2704m1 97344gn1 10816bn1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 10816bo1

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	-3	-3	0	-	-3	6	-6	0	0	-3	0	1	-3	6	-6	8	12	15	6	-10	-6	-6	12

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Quadratic twists for elliptic curve 10816bo1

-4	8	-3	13
10816t1	2704m1	97344gn1	10816bn1

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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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