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	76176w	Isogeny class
Conductor	76176	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-141915888 = -1 · 24 · 36 · 233	Discriminant
Eigenvalues	2+ 3- -2 -2 -6 -1 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,69,529]	[a1,a2,a3,a4,a6]
Generators	[0:23:1]	Generators of the group modulo torsion
j	256	j-invariant
L	2.6214787877091	L(r)(E,1)/r!
Ω	1.3092172880819	Real period
R	1.0011626065468	Regulator
r	1	Rank of the group of rational points
S	1.000000000902	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38088m1 8464c1 76176k1	Quadratic twists by: -4 -3 -23

Hecke Eigenvalues for elliptic curve 76176w1

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	-6	-1	-6	4	-	-9	-3	-2	1	0	-1	12	-12	8	10	-13	5	4	2	12	-2

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Quadratic twists for elliptic curve 76176w1

-4	-3	-23
38088m1	8464c1	76176k1

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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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