Cremona's table of elliptic curves

799 = 17 · 47

Field	Data	Notes
Atkin-Lehner	17- 47-	Signs for the Atkin-Lehner involutions
Class	799b	Isogeny class
Conductor	799	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	10852817 = 173 · 472	Discriminant
Eigenvalues	-1  2  0 -2  0 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-118,418]	[a1,a2,a3,a4,a6]
Generators	[-2:26:1]	Generators of the group modulo torsion
j	181802454625/10852817	j-invariant
L	1.9428746695879	L(r)(E,1)/r!
Ω	2.239883143538	Real period
R	0.57826667585852	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12784d1 51136f1 7191c1 19975a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 799b1

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	2	0	-2	0	-6	-	-4	4	-4	0	6	4	-12	-	-10	-12	14	4	-6	8	2	16	-10	-6

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Quadratic twists for elliptic curve 799b1

-4	8	-3	5	-7	-11	17	-47
12784d1	51136f1	7191c1	19975a1	39151c1	96679c1	13583d1	37553b1

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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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