Cremona's table of elliptic curves

4761 = 3² · 23²

Field	Data	Notes
Atkin-Lehner	3- 23-	Signs for the Atkin-Lehner involutions
Class	4761g	Isogeny class
Conductor	4761	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-843396867 = -1 · 313 · 232	Discriminant
Eigenvalues	2 3-  0 -1  4 -3 -8  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-345,-2835]	[a1,a2,a3,a4,a6]
Generators	[1074:12313:8]	Generators of the group modulo torsion
j	-11776000/2187	j-invariant
L	6.9802988683065	L(r)(E,1)/r!
Ω	0.54835395492041	Real period
R	6.3647748007213	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	76176bp1 1587e1 119025bt1 4761f1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 4761g1

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	-	0	-1	4	-3	-8	4	-	4	-8	1	-8	-1	6	6	-6	-15	13	10	-14	8	-6	2	-2

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Quadratic twists for elliptic curve 4761g1

-4	-3	5	-23
76176bp1	1587e1	119025bt1	4761f1

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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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