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	5073f	Isogeny class
Conductor	5073	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	352	Modular degree for the optimal curve
Δ	-15219 = -1 · 32 · 19 · 89	Discriminant
Eigenvalues	1 3- -1  0  3 -7  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4,-7]	[a1,a2,a3,a4,a6]
Generators	[7:14:1]	Generators of the group modulo torsion
j	-4826809/15219	j-invariant
L	5.0851544785624	L(r)(E,1)/r!
Ω	1.6073724314803	Real period
R	1.5818221026347	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	81168bg1 15219h1 126825c1 96387e1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 5073f1

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
1	-	-1	0	3	-7	3	-	6	9	3	-11	1	-8	-8	4	-3	-10	2	-6	-11	-10	10	+	-16

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Quadratic twists for elliptic curve 5073f1

-4	-3	5	-19
81168bg1	15219h1	126825c1	96387e1

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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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