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	76176i	Isogeny class
Conductor	76176	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	3831728976 = 24 · 39 · 233	Discriminant
Eigenvalues	2+ 3-  2  2  0  2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1794,29095]	[a1,a2,a3,a4,a6]
Generators	[11921:32040:343]	Generators of the group modulo torsion
j	4499456/27	j-invariant
L	8.5558487941385	L(r)(E,1)/r!
Ω	1.4037660665026	Real period
R	6.094924928859	Regulator
r	1	Rank of the group of rational points
S	1.0000000001316	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38088d1 25392p1 76176u1	Quadratic twists by: -4 -3 -23

Hecke Eigenvalues for elliptic curve 76176i1

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	0	2	-6	2	-	6	0	-4	-2	-6	-4	6	0	4	-10	8	-10	-10	16	6	-4

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Quadratic twists for elliptic curve 76176i1

-4	-3	-23
38088d1	25392p1	76176u1

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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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