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	8	Product of Tamagawa factors cp
Δ	17969614533 = 314 · 13 · 172	Discriminant
Eigenvalues	1 3-  0 -2  2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-882,-7533]	[a1,a2,a3,a4,a6]
j	104154702625/24649677	j-invariant
L	1.7820407287574	L(r)(E,1)/r!
Ω	0.89102036437871	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	31824r2 127296u2 663c2 49725q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1989a2

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 1989a2

-4	8	-3	5	-7	13	17
31824r2	127296u2	663c2	49725q2	97461v2	25857f2	33813e2

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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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