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	5037g	Isogeny class
Conductor	5037	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5568	Modular degree for the optimal curve
Δ	16668989433 = 34 · 232 · 733	Discriminant
Eigenvalues	1 3-  0 -2 -2  6  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8036,276509]	[a1,a2,a3,a4,a6]
j	57380695289277625/16668989433	j-invariant
L	2.4159177807741	L(r)(E,1)/r!
Ω	1.2079588903871	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	80592p1 15111i1 125925l1 115851s1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5037g1

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

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Quadratic twists for elliptic curve 5037g1

-4	-3	5	-23
80592p1	15111i1	125925l1	115851s1

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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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