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	890f	Isogeny class
Conductor	890	Conductor
∏ cp	13	Product of Tamagawa factors cp
deg	312	Modular degree for the optimal curve
Δ	-3645440 = -1 · 213 · 5 · 89	Discriminant
Eigenvalues	2- -3 5+  0  3 -4 -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,12,87]	[a1,a2,a3,a4,a6]
Generators	[5:-19:1]	Generators of the group modulo torsion
j	206425071/3645440	j-invariant
L	2.1818938579773	L(r)(E,1)/r!
Ω	1.8577167477569	Real period
R	0.090346383149009	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7120m1 28480y1 8010g1 4450d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 890f1

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
-	-3	+	0	3	-4	-4	2	-4	2	-8	-10	-12	7	-3	1	0	-5	-4	-14	-4	12	11	-	16

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Quadratic twists for elliptic curve 890f1

-4	8	-3	5	-7	-11	89
7120m1	28480y1	8010g1	4450d1	43610bc1	107690l1	79210f1

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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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