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
Δ	158420 = 22 · 5 · 892	Discriminant
Eigenvalues	2+ -2 5+ -2  4  4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-109,-444]	[a1,a2,a3,a4,a6]
Generators	[-6:3:1]	Generators of the group modulo torsion
j	141339344329/158420	j-invariant
L	1.2590202824938	L(r)(E,1)/r!
Ω	1.4792803968835	Real period
R	0.85110320203403	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	7120i2 28480o2 8010m2 4450i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 890b2

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 890b2

-4	8	-3	5	-7	-11	89
7120i2	28480o2	8010m2	4450i2	43610p2	107690z2	79210b2

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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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