Cremona's table of elliptic curves

5159 = 7 · 11 · 67

Field	Data	Notes
Atkin-Lehner	7+ 11- 67-	Signs for the Atkin-Lehner involutions
Class	5159f	Isogeny class
Conductor	5159	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	12482566789 = 73 · 112 · 673	Discriminant
Eigenvalues	1 -1  1 7+ 11-  1  4  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-23422,-1389493]	[a1,a2,a3,a4,a6]
Generators	[202:1373:1]	Generators of the group modulo torsion
j	1421099916246680041/12482566789	j-invariant
L	3.8679755619509	L(r)(E,1)/r!
Ω	0.38591474740676	Real period
R	1.6704792910622	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	82544w1 46431f1 128975h1 36113f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5159f1

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	-1	1	+	-	1	4	6	-7	3	1	-3	1	-6	8	0	-4	6	-	-15	-2	-4	0	-6	-10

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Quadratic twists for elliptic curve 5159f1

-4	-3	5	-7	-11
82544w1	46431f1	128975h1	36113f1	56749k1

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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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