Cremona's table of elliptic curves

89 = Prime conductor

Field	Data	Notes
Atkin-Lehner	89+	Signs for the Atkin-Lehner involutions
Class	89a	Isogeny class
Conductor	89	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	-89 = Prime discriminant	Discriminant
Eigenvalues	-1 -1 -1 -4 -2  2  3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1,0]	[a1,a2,a3,a4,a6]
Generators	[0:0:1]	Generators of the group modulo torsion
j	-117649/89	j-invariant
L	0.62247654153697	L(r)(E,1)/r!
Ω	5.5526265645768	Real period
R	0.1121048812301	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	1424b1 5696a1 801d1 2225a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 89a1

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	-1	-1	-4	-2	2	3	-5	7	0	-9	-2	0	-7	-12	-3	4	6	12	-10	7	-6	12	+	9

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Quadratic twists for elliptic curve 89a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	89
1424b1	5696a1	801d1	2225a1	4361c1	10769a1	15041e1	25721c1	32129b1	47081b1	74849c1	85529d1	121841c1	7921b1

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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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