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	76176x	Isogeny class
Conductor	76176	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	-81743551488 = -1 · 210 · 38 · 233	Discriminant
Eigenvalues	2+ 3- -2  4 -2  6  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,69,13754]	[a1,a2,a3,a4,a6]
Generators	[-11:108:1]	Generators of the group modulo torsion
j	4/9	j-invariant
L	6.5698217042164	L(r)(E,1)/r!
Ω	0.8487809464936	Real period
R	0.96753787451015	Regulator
r	1	Rank of the group of rational points
S	1.0000000001606	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38088o1 25392b1 76176m1	Quadratic twists by: -4 -3 -23

Hecke Eigenvalues for elliptic curve 76176x1

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	4	-2	6	0	-6	-	-6	4	2	-6	-2	4	14	-4	-10	2	4	2	-12	-6	-12	12

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Quadratic twists for elliptic curve 76176x1

-4	-3	-23
38088o1	25392b1	76176m1

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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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