Cremona's table of elliptic curves

10769 = 11² · 89

Field	Data	Notes
Atkin-Lehner	11- 89-	Signs for the Atkin-Lehner involutions
Class	10769d	Isogeny class
Conductor	10769	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3200	Modular degree for the optimal curve
Δ	157668929 = 116 · 89	Discriminant
Eigenvalues	-1  2 -2 -2 11- -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-184,-824]	[a1,a2,a3,a4,a6]
Generators	[94:860:1]	Generators of the group modulo torsion
j	389017/89	j-invariant
L	2.9332782122852	L(r)(E,1)/r!
Ω	1.3175406166657	Real period
R	2.2263284905087	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	96921r1 89b2	Quadratic twists by: -3 -11

Hecke Eigenvalues for elliptic curve 10769d1

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	-2	-2	-	-2	-6	2	2	6	6	10	6	-2	12	-6	-10	6	12	4	-10	12	6	-	-18

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Quadratic twists for elliptic curve 10769d1

-3	-11
96921r1	89b2

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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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