Cremona's table of elliptic curves

126405 = 3² · 5 · 53²

Field	Data	Notes
Atkin-Lehner	3- 5- 53+	Signs for the Atkin-Lehner involutions
Class	126405s	Isogeny class
Conductor	126405	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2650286304620300025 = 314 · 52 · 536	Discriminant
Eigenvalues	-1 3- 5-  0  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3413462,2426985524]	[a1,a2,a3,a4,a6]
Generators	[13881186:140326663:10648]	Generators of the group modulo torsion
j	272223782641/164025	j-invariant
L	4.395060527252	L(r)(E,1)/r!
Ω	0.25318048509037	Real period
R	8.6796984945238	Regulator
r	1	Rank of the group of rational points
S	0.99999999469601	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	42135f6 45a5	Quadratic twists by: -3 53

Hecke Eigenvalues for elliptic curve 126405s6

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
-1	-	-	0	4	-2	-2	-4	0	2	0	-10	10	4	-8	+	4	2	-12	-8	-10	0	12	6	2

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Quadratic twists for elliptic curve 126405s6

-3	53
42135f6	45a5

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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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