Cremona's table of elliptic curves

890 = 2 · 5 · 89

Field	Data	Notes
Atkin-Lehner	2+ 5+ 89+	Signs for the Atkin-Lehner involutions
Class	890b	Isogeny class
Conductor	890	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	35600 = 24 · 52 · 89	Discriminant
Eigenvalues	2+ -2 5+ -2  4  4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-9,-4]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	68417929/35600	j-invariant
L	1.2590202824938	L(r)(E,1)/r!
Ω	2.9585607937671	Real period
R	0.42555160101702	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7120i1 28480o1 8010m1 4450i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 890b1

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

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Quadratic twists for elliptic curve 890b1

-4	8	-3	5	-7	-11	89
7120i1	28480o1	8010m1	4450i1	43610p1	107690z1	79210b1

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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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