Cremona's table of elliptic curves

4743 = 3² · 17 · 31

Field	Data	Notes
Atkin-Lehner	3- 17- 31+	Signs for the Atkin-Lehner involutions
Class	4743c	Isogeny class
Conductor	4743	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1600	Modular degree for the optimal curve
Δ	-2894050539 = -1 · 311 · 17 · 312	Discriminant
Eigenvalues	0 3- -1 -2 -1  1 17-  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1128,-14810]	[a1,a2,a3,a4,a6]
Generators	[64:418:1]	Generators of the group modulo torsion
j	-217732612096/3969891	j-invariant
L	2.6475918138526	L(r)(E,1)/r!
Ω	0.41145521210722	Real period
R	1.6086755836032	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	75888bb1 1581a1 118575g1 80631d1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 4743c1

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
0	-	-1	-2	-1	1	-	3	3	-6	+	4	9	-1	0	2	8	6	-4	16	-4	-12	4	12	12

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Quadratic twists for elliptic curve 4743c1

-4	-3	5	17
75888bb1	1581a1	118575g1	80631d1

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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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