Cremona's table of elliptic curves

127296 = 2⁶ · 3² · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 17-	Signs for the Atkin-Lehner involutions
Class	127296dp	Isogeny class
Conductor	127296	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	589824	Modular degree for the optimal curve
Δ	634688910655488 = 220 · 36 · 132 · 173	Discriminant
Eigenvalues	2- 3-  2 -4  2 13- 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-53964,4670352]	[a1,a2,a3,a4,a6]
Generators	[96:612:1]	Generators of the group modulo torsion
j	90942871473/3321188	j-invariant
L	7.7649599748737	L(r)(E,1)/r!
Ω	0.50913785421783	Real period
R	1.2709327961963	Regulator
r	1	Rank of the group of rational points
S	1.0000000018478	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	127296bo1 31824bg1 14144r1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 127296dp1

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	-	-	0	2	8	8	6	-12	4	-8	-6	4	8	-8	-8	8	10	0	-6	-16

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Quadratic twists for elliptic curve 127296dp1

-4	8	-3
127296bo1	31824bg1	14144r1

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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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