Cremona's table of elliptic curves

5073 = 3 · 19 · 89

Field	Data	Notes
Atkin-Lehner	3- 19- 89+	Signs for the Atkin-Lehner involutions
Class	5073h	Isogeny class
Conductor	5073	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1248	Modular degree for the optimal curve
Δ	-96387 = -1 · 3 · 192 · 89	Discriminant
Eigenvalues	2 3-  2 -4  0 -6  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-62,-211]	[a1,a2,a3,a4,a6]
Generators	[2382:5041:216]	Generators of the group modulo torsion
j	-26784575488/96387	j-invariant
L	8.2881789436886	L(r)(E,1)/r!
Ω	0.84936803499537	Real period
R	4.8790268777502	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	81168bj1 15219i1 126825e1 96387f1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 5073h1

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	0	-6	0	-	-7	5	-6	8	-1	-4	-4	4	9	-2	-7	-14	-15	-7	5	+	13

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Quadratic twists for elliptic curve 5073h1

-4	-3	5	-19
81168bj1	15219i1	126825e1	96387f1

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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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