Cremona's table of elliptic curves

129605 = 5 · 7² · 23²

Field	Data	Notes
Atkin-Lehner	5+ 7- 23-	Signs for the Atkin-Lehner involutions
Class	129605p	Isogeny class
Conductor	129605	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	21288960	Modular degree for the optimal curve
Δ	-5.2240911028021E+24	Discriminant
Eigenvalues	2  1 5+ 7-  3  1  5  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,41309434,-40598475599]	[a1,a2,a3,a4,a6]
Generators	[10266887850553289242899747108740854703463822560789409799712248176:1725950003318378281367162920058647458766763426156576344562863127419:383477274358882566408273501253693653476298438648844659585024]	Generators of the group modulo torsion
j	1305034698752/874503125	j-invariant
L	16.649308659562	L(r)(E,1)/r!
Ω	0.043483409434632	Real period
R	95.722189658282	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	129605bg1 5635f1	Quadratic twists by: -7 -23

Hecke Eigenvalues for elliptic curve 129605p1

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	1	+	-	3	1	5	2	-	-1	-2	-4	2	6	-3	-2	-6	4	-2	8	-6	-3	-12	16	1

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Quadratic twists for elliptic curve 129605p1

-7	-23
129605bg1	5635f1

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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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