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	5159a	Isogeny class
Conductor	5159	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-115407433603 = -1 · 76 · 114 · 67	Discriminant
Eigenvalues	0  0 -2 7+ 11+  4  1 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-5036,-138523]	[a1,a2,a3,a4,a6]
Generators	[113:857:1]	Generators of the group modulo torsion
j	-14124753468260352/115407433603	j-invariant
L	2.3998447953335	L(r)(E,1)/r!
Ω	0.28322808440559	Real period
R	2.1182969905421	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	82544bj1 46431g1 128975e1 36113a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5159a1

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	0	-2	+	+	4	1	-7	9	3	2	-1	0	8	-3	2	7	8	+	-16	-9	14	4	-11	16

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Quadratic twists for elliptic curve 5159a1

-4	-3	5	-7	-11
82544bj1	46431g1	128975e1	36113a1	56749b1

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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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