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	890a	Isogeny class
Conductor	890	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	8900 = 22 · 52 · 89	Discriminant
Eigenvalues	2+  0 5+  2  4 -6 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	15438249/8900	j-invariant
L	1.767463943197	L(r)(E,1)/r!
Ω	3.4473615420015	Real period
R	0.51270048750698	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	7120h1 28480i1 8010l1 4450h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 890a1

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
+	0	+	2	4	-6	-6	-2	6	0	-4	-10	2	0	4	-10	-10	-4	4	8	-14	0	0	+	-10

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Quadratic twists for elliptic curve 890a1

-4	8	-3	5	-7	-11	89
7120h1	28480i1	8010l1	4450h1	43610o1	107690x1	79210a1

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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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