Cremona's table of elliptic curves

127449 = 3² · 7² · 17²

Field	Data	Notes
Atkin-Lehner	3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	127449bj	Isogeny class
Conductor	127449	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	290304	Modular degree for the optimal curve
Δ	8501738276367 = 36 · 79 · 172	Discriminant
Eigenvalues	1 3- -4 7-  0  2 17+  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5154,-23311]	[a1,a2,a3,a4,a6]
Generators	[-40:363:1]	Generators of the group modulo torsion
j	610929/343	j-invariant
L	6.0633999393591	L(r)(E,1)/r!
Ω	0.60596520411978	Real period
R	2.5015462929652	Regulator
r	1	Rank of the group of rational points
S	0.99999998338096	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14161c1 18207f1 127449bv1	Quadratic twists by: -3 -7 17

Hecke Eigenvalues for elliptic curve 127449bj1

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	-	-4	-	0	2	+	7	4	3	7	-10	0	-2	3	3	-9	8	-8	2	6	-6	-1	-8	2

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Quadratic twists for elliptic curve 127449bj1

-3	-7	17
14161c1	18207f1	127449bv1

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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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