Cremona's table of elliptic curves

747 = 3² · 83

Field	Data	Notes
Atkin-Lehner	3+ 83+	Signs for the Atkin-Lehner involutions
Class	747a	Isogeny class
Conductor	747	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	84	Modular degree for the optimal curve
Δ	1633689 = 39 · 83	Discriminant
Eigenvalues	-1 3+ -2  0  0  6 -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-56,-134]	[a1,a2,a3,a4,a6]
Generators	[-4:5:1]	Generators of the group modulo torsion
j	970299/83	j-invariant
L	1.4144734402638	L(r)(E,1)/r!
Ω	1.7571979728231	Real period
R	1.609919271636	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	11952j1 47808e1 747b1 18675c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 747a1

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

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Quadratic twists for elliptic curve 747a1

-4	8	-3	5	-7	-11	13	-83
11952j1	47808e1	747b1	18675c1	36603b1	90387d1	126243e1	62001c1

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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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