Cremona's table of elliptic curves

747 = 3² · 83

Field	Data	Notes
Atkin-Lehner	3- 83-	Signs for the Atkin-Lehner involutions
Class	747d	Isogeny class
Conductor	747	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	60	Modular degree for the optimal curve
Δ	-60507 = -1 · 36 · 83	Discriminant
Eigenvalues	1 3-  2 -3 -3 -6 -5  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,9,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	103823/83	j-invariant
L	2.7052674428119	L(r)(E,1)/r!
Ω	2.2599386817377	Real period
R	1.1970534708188	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	11952o1 47808o1 83a1 18675j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 747d1

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	-3	-3	-6	-5	2	4	7	5	-11	2	-8	0	-6	-5	5	-2	-2	0	14	-	0	-8

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Quadratic twists for elliptic curve 747d1

-4	8	-3	5	-7	-11	13	-83
11952o1	47808o1	83a1	18675j1	36603n1	90387n1	126243l1	62001k1

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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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