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	1989a	Isogeny class
Conductor	1989	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	169647777 = 310 · 132 · 17	Discriminant
Eigenvalues	1 3-  0 -2  2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-297,1944]	[a1,a2,a3,a4,a6]
j	3981876625/232713	j-invariant
L	1.7820407287574	L(r)(E,1)/r!
Ω	1.7820407287574	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	31824r1 127296u1 663c1 49725q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1989a1

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

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Quadratic twists for elliptic curve 1989a1

-4	8	-3	5	-7	13	17
31824r1	127296u1	663c1	49725q1	97461v1	25857f1	33813e1

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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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