Cremona's table of elliptic curves

4761 = 3² · 23²

Field	Data	Notes
Atkin-Lehner	3- 23-	Signs for the Atkin-Lehner involutions
Class	4761d	Isogeny class
Conductor	4761	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	70656	Modular degree for the optimal curve
Δ	-106356263506728687 = -1 · 310 · 239	Discriminant
Eigenvalues	-1 3-  4 -4  0 -2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-326228,73496094]	[a1,a2,a3,a4,a6]
Generators	[14:8295:1]	Generators of the group modulo torsion
j	-2924207/81	j-invariant
L	2.7281536640804	L(r)(E,1)/r!
Ω	0.33374287960479	Real period
R	4.0872087927554	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	76176ck1 1587b1 119025bb1 4761e1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 4761d1

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	-	4	-4	0	-2	4	-4	-	-2	-8	8	6	-4	0	-4	4	-8	-12	-8	6	4	0	12	-8

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Quadratic twists for elliptic curve 4761d1

-4	-3	5	-23
76176ck1	1587b1	119025bb1	4761e1

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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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