Cremona's table of elliptic curves

1989 = 3² · 13 · 17

Field	Data	Notes
Atkin-Lehner	3- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	1989b	Isogeny class
Conductor	1989	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	59818643937 = 36 · 136 · 17	Discriminant
Eigenvalues	1 3- -4 -2 -6 13+ 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-6594,-204121]	[a1,a2,a3,a4,a6]
j	43499078731809/82055753	j-invariant
L	0.52985671811654	L(r)(E,1)/r!
Ω	0.52985671811654	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31824ba1 127296bf1 221a1 49725s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1989b1

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	-	-4	-2	-6	+	+	8	-4	6	-2	-8	0	4	0	6	0	-10	-8	-2	0	0	4	2	-4

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Quadratic twists for elliptic curve 1989b1

-4	8	-3	5	-7	13	17
31824ba1	127296bf1	221a1	49725s1	97461w1	25857j1	33813i1

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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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