Cremona's table of elliptic curves

899 = 29 · 31

Field	Data	Notes
Atkin-Lehner	29+ 31+	Signs for the Atkin-Lehner involutions
Class	899a	Isogeny class
Conductor	899	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	28	Modular degree for the optimal curve
Δ	899 = 29 · 31	Discriminant
Eigenvalues	1 -2  1  2  0  2 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3,-1]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	1771561/899	j-invariant
L	2.3407393198619	L(r)(E,1)/r!
Ω	3.9981065198805	Real period
R	0.58546197011575	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	14384e1 57536j1 8091e1 22475b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 899a1

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	1	2	0	2	-3	-5	-1	+	+	-3	-10	-6	-9	-10	8	-7	-2	14	-11	4	9	13	2

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Quadratic twists for elliptic curve 899a1

-4	8	-3	5	-7	-11	29	-31
14384e1	57536j1	8091e1	22475b1	44051g1	108779e1	26071a1	27869f1

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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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