Cremona's table of elliptic curves

7139 = 11² · 59

Field	Data	Notes
Atkin-Lehner	11- 59-	Signs for the Atkin-Lehner involutions
Class	7139c	Isogeny class
Conductor	7139	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	2904	Modular degree for the optimal curve
Δ	-12647173979 = -1 · 118 · 59	Discriminant
Eigenvalues	0  1  2  3 11-  2 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-887,-11819]	[a1,a2,a3,a4,a6]
Generators	[3044:15093:64]	Generators of the group modulo torsion
j	-360448/59	j-invariant
L	4.8875807998653	L(r)(E,1)/r!
Ω	0.43347723857148	Real period
R	3.7584294052534	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	114224l1 64251k1 7139d1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 7139c1

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	2	3	-	2	-2	-5	4	-3	-2	-8	-9	-6	-6	2	-	-4	4	-9	4	8	8	-6	8

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Quadratic twists for elliptic curve 7139c1

-4	-3	-11
114224l1	64251k1	7139d1

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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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