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	5037d	Isogeny class
Conductor	5037	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	76114107 = 33 · 232 · 732	Discriminant
Eigenvalues	-1 3+ -2  0  4 -2 -6  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-109,80]	[a1,a2,a3,a4,a6]
Generators	[-5:25:1]	Generators of the group modulo torsion
j	143301984337/76114107	j-invariant
L	1.6997933371186	L(r)(E,1)/r!
Ω	1.6958492983854	Real period
R	1.0023257011911	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	80592bb2 15111f2 125925v2 115851f2	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5037d2

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	+	-2	0	4	-2	-6	6	+	0	-10	2	-2	8	4	10	0	2	-2	8	+	14	12	-12	-10

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Quadratic twists for elliptic curve 5037d2

-4	-3	5	-23
80592bb2	15111f2	125925v2	115851f2

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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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