Cremona's table of elliptic curves

5890 = 2 · 5 · 19 · 31

Field	Data	Notes
Atkin-Lehner	2- 5+ 19- 31+	Signs for the Atkin-Lehner involutions
Class	5890f	Isogeny class
Conductor	5890	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-1790560000 = -1 · 28 · 54 · 192 · 31	Discriminant
Eigenvalues	2-  0 5+ -4  2  0  6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,302,-303]	[a1,a2,a3,a4,a6]
Generators	[3:23:1]	Generators of the group modulo torsion
j	3055568514831/1790560000	j-invariant
L	4.9103904381744	L(r)(E,1)/r!
Ω	0.87540401371073	Real period
R	0.70116060145758	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	47120h1 53010ba1 29450e1 111910c1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 5890f1

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

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Quadratic twists for elliptic curve 5890f1

-4	-3	5	-19
47120h1	53010ba1	29450e1	111910c1

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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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