Cremona's table of elliptic curves

731 = 17 · 43

Field	Data	Notes
Atkin-Lehner	17+ 43+	Signs for the Atkin-Lehner involutions
Class	731a	Isogeny class
Conductor	731	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-211259 = -1 · 173 · 43	Discriminant
Eigenvalues	1  1 -1  0 -6  1 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-539,4765]	[a1,a2,a3,a4,a6]
Generators	[13:-5:1]	Generators of the group modulo torsion
j	-17271547035049/211259	j-invariant
L	2.8068624879322	L(r)(E,1)/r!
Ω	2.8737517466439	Real period
R	0.97672406505196	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	11696l1 46784h1 6579d1 18275b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 731a1

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	0	-6	1	+	-2	2	6	2	-3	-4	+	13	1	-3	-7	-9	11	-7	-8	-9	2	10

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Quadratic twists for elliptic curve 731a1

-4	8	-3	5	-7	-11	13	17	-43
11696l1	46784h1	6579d1	18275b1	35819g1	88451g1	123539b1	12427a1	31433a1

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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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