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	127296cj	Isogeny class
Conductor	127296	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	399430061354668032 = 212 · 312 · 133 · 174	Discriminant
Eigenvalues	2- 3- -4  2  4 13+ 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-199092,-15636800]	[a1,a2,a3,a4,a6]
Generators	[800:18360:1]	Generators of the group modulo torsion
j	292279034436544/133768319373	j-invariant
L	4.8545028792609	L(r)(E,1)/r!
Ω	0.23605701998685	Real period
R	5.14123967234	Regulator
r	1	Rank of the group of rational points
S	1.0000000030689	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	127296ck2 63648u1 42432ch2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 127296cj2

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
-	-	-4	2	4	+	+	-2	-8	-10	2	2	4	4	0	-6	-4	-2	2	-8	-6	12	4	12	-14

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Quadratic twists for elliptic curve 127296cj2

-4	8	-3
127296ck2	63648u1	42432ch2

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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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