Cremona's table of elliptic curves

76176 = 2⁴ · 3² · 23²

Field	Data	Notes
Atkin-Lehner	2+ 3- 23-	Signs for the Atkin-Lehner involutions
Class	76176v	Isogeny class
Conductor	76176	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	8478720	Modular degree for the optimal curve
Δ	-1.984863132068E+22	Discriminant
Eigenvalues	2+ 3- -2 -2  4 -6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-35442471,-81496975066]	[a1,a2,a3,a4,a6]
Generators	[54017235048759322193:3705988118761843411464:5746592743594613]	Generators of the group modulo torsion
j	-14647977776/59049	j-invariant
L	3.6019648796958	L(r)(E,1)/r!
Ω	0.030930275195563	Real period
R	29.113585767536	Regulator
r	1	Rank of the group of rational points
S	1.000000000227	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38088l1 25392a1 76176j1	Quadratic twists by: -4 -3 -23

Hecke Eigenvalues for elliptic curve 76176v1

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	-2	4	-6	-6	-6	-	6	-8	8	6	10	4	2	8	8	-10	-8	-10	-6	12	-18	-12

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Quadratic twists for elliptic curve 76176v1

-4	-3	-23
38088l1	25392a1	76176j1

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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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