Cremona's table of elliptic curves

899 = 29 · 31

Field	Data	Notes
Atkin-Lehner	29- 31+	Signs for the Atkin-Lehner involutions
Class	899b	Isogeny class
Conductor	899	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	58	Modular degree for the optimal curve
Δ	-899 = -1 · 29 · 31	Discriminant
Eigenvalues	2  1  2  5 -3  2 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-2,1]	[a1,a2,a3,a4,a6]
j	-1404928/899	j-invariant
L	4.6049071056349	L(r)(E,1)/r!
Ω	4.6049071056349	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14384i1 57536b1 8091d1 22475e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 899b1

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
2	1	2	5	-3	2	-3	-2	4	-	+	-6	-2	0	6	-8	4	11	7	-8	1	-8	12	-7	8

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Quadratic twists for elliptic curve 899b1

-4	8	-3	5	-7	-11	29	-31
14384i1	57536b1	8091d1	22475e1	44051l1	108779a1	26071b1	27869c1

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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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