Cremona's table of elliptic curves

747 = 3² · 83

Field	Data	Notes
Atkin-Lehner	3+ 83-	Signs for the Atkin-Lehner involutions
Class	747b	Isogeny class
Conductor	747	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	186003 = 33 · 832	Discriminant
Eigenvalues	1 3+  2  0  0  6  4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-21,-26]	[a1,a2,a3,a4,a6]
j	38958219/6889	j-invariant
L	2.2522275159788	L(r)(E,1)/r!
Ω	2.2522275159788	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	11952h2 47808b2 747a2 18675b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 747b2

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 747b2

-4	8	-3	5	-7	-11	13	-83
11952h2	47808b2	747a2	18675b2	36603a2	90387b2	126243a2	62001d2

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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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