Cremona's table of elliptic curves

5037 = 3 · 23 · 73

Field	Data	Notes
Atkin-Lehner	3- 23- 73+	Signs for the Atkin-Lehner involutions
Class	5037h	Isogeny class
Conductor	5037	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1984	Modular degree for the optimal curve
Δ	-9927927 = -1 · 34 · 23 · 732	Discriminant
Eigenvalues	1 3-  4 -2 -2 -2  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-219,-1271]	[a1,a2,a3,a4,a6]
Generators	[317:5481:1]	Generators of the group modulo torsion
j	-1153990560169/9927927	j-invariant
L	6.158040299348	L(r)(E,1)/r!
Ω	0.62054514264944	Real period
R	4.9617988089118	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	80592n1 15111d1 125925d1 115851t1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5037h1

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	-	4	-2	-2	-2	0	-8	-	-6	-8	2	10	-6	-4	0	0	-10	0	-16	+	16	-2	-2	-14

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Quadratic twists for elliptic curve 5037h1

-4	-3	5	-23
80592n1	15111d1	125925d1	115851t1

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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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