Cremona's table of elliptic curves

5194 = 2 · 7² · 53

Field	Data	Notes
Atkin-Lehner	2- 7- 53+	Signs for the Atkin-Lehner involutions
Class	5194n	Isogeny class
Conductor	5194	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-4483898924288 = -1 · 28 · 76 · 533	Discriminant
Eigenvalues	2- -1  0 7-  0 -5  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1205548,508975053]	[a1,a2,a3,a4,a6]
Generators	[629:-119:1]	Generators of the group modulo torsion
j	-1646982616152408625/38112512	j-invariant
L	4.6152380366203	L(r)(E,1)/r!
Ω	0.5615676957549	Real period
R	0.51365557433108	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	41552be2 46746n2 129850f2 106c2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5194n2

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	0	-	0	-5	3	1	3	9	4	5	-6	-10	-6	+	-6	-8	-4	-3	4	-13	-3	-18	7

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Quadratic twists for elliptic curve 5194n2

-4	-3	5	-7
41552be2	46746n2	129850f2	106c2

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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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