Cremona's table of elliptic curves

7139 = 11² · 59

Field	Data	Notes
Atkin-Lehner	11- 59+	Signs for the Atkin-Lehner involutions
Class	7139a	Isogeny class
Conductor	7139	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	38148	Modular degree for the optimal curve
Δ	-1530308051459 = -1 · 1110 · 59	Discriminant
Eigenvalues	2  3  3 -1 11-  0  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-14641,-684467]	[a1,a2,a3,a4,a6]
j	-13381632/59	j-invariant
L	10.630614858556	L(r)(E,1)/r!
Ω	0.216951323644	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	49	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	114224x1 64251bd1 7139b1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 7139a1

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
2	3	3	-1	-	0	2	4	6	-6	6	-10	-6	0	4	3	+	-2	10	-9	-2	15	-4	-10	12

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Quadratic twists for elliptic curve 7139a1

-4	-3	-11
114224x1	64251bd1	7139b1

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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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