Cremona's table of elliptic curves

4731 = 3 · 19 · 83

Field	Data	Notes
Atkin-Lehner	3+ 19- 83+	Signs for the Atkin-Lehner involutions
Class	4731b	Isogeny class
Conductor	4731	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2208	Modular degree for the optimal curve
Δ	-425264859 = -1 · 32 · 193 · 832	Discriminant
Eigenvalues	-2 3+ -1 -1 -3 -4 -5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-76,1050]	[a1,a2,a3,a4,a6]
Generators	[170:737:8] [12:41:1]	Generators of the group modulo torsion
j	-49188818944/425264859	j-invariant
L	2.1565358948397	L(r)(E,1)/r!
Ω	1.4349405569146	Real period
R	0.12523956041525	Regulator
r	2	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75696k1 14193b1 118275i1 89889h1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4731b1

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
-2	+	-1	-1	-3	-4	-5	-	0	-8	0	-6	-2	1	-7	-8	-12	11	2	6	3	6	+	6	-6

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Quadratic twists for elliptic curve 4731b1

-4	-3	5	-19
75696k1	14193b1	118275i1	89889h1

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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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