Cremona's table of elliptic curves

89 = Prime conductor

Field	Data	Notes
Atkin-Lehner	89-	Signs for the Atkin-Lehner involutions
Class	89b	Isogeny class
Conductor	89	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5	Modular degree for the optimal curve
Δ	-7921 = -1 · 892	Discriminant
Eigenvalues	1  2 -2  2 -4  2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,4,5]	[a1,a2,a3,a4,a6]
j	4657463/7921	j-invariant
L	1.4223048292271	L(r)(E,1)/r!
Ω	2.8446096584542	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	1424f2 5696g2 801b2 2225b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 89b1

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	2	-2	2	-4	2	6	-2	2	-6	6	10	-6	2	12	-6	-10	-6	12	4	10	-12	-6	-	-18

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Quadratic twists for elliptic curve 89b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	89
1424f2	5696g2	801b2	2225b2	4361b2	10769d2	15041a2	25721e2	32129a2	47081a2	74849a2	85529b2	121841b2	7921a2

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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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