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	890g	Isogeny class
Conductor	890	Conductor
∏ cp	25	Product of Tamagawa factors cp
deg	200	Modular degree for the optimal curve
Δ	-8900000 = -1 · 25 · 55 · 89	Discriminant
Eigenvalues	2- -1 5- -2 -3 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,10,147]	[a1,a2,a3,a4,a6]
Generators	[-5:3:1]	Generators of the group modulo torsion
j	109902239/8900000	j-invariant
L	2.8194525619231	L(r)(E,1)/r!
Ω	1.7698498471179	Real period
R	1.5930461934466	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	7120n1 28480c1 8010f1 4450a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 890g1

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	-3	-6	-2	0	4	-10	-8	8	2	9	3	-11	0	7	-2	-8	-16	0	9	+	-2

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Quadratic twists for elliptic curve 890g1

-4	8	-3	5	-7	-11	89
7120n1	28480c1	8010f1	4450a1	43610w1	107690r1	79210h1

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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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