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	127449bl	Isogeny class
Conductor	127449	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	589824	Modular degree for the optimal curve
Δ	-923435587508679 = -1 · 38 · 73 · 177	Discriminant
Eigenvalues	-1 3-  2 7- -6  4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-11759,-1539282]	[a1,a2,a3,a4,a6]
Generators	[3742:76155:8]	Generators of the group modulo torsion
j	-29791/153	j-invariant
L	5.0511353528634	L(r)(E,1)/r!
Ω	0.20667773276569	Real period
R	3.0549585349856	Regulator
r	1	Rank of the group of rational points
S	1.0000000243967	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	42483k1 127449bm1 7497g1	Quadratic twists by: -3 -7 17

Hecke Eigenvalues for elliptic curve 127449bl1

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

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Quadratic twists for elliptic curve 127449bl1

-3	-7	17
42483k1	127449bm1	7497g1

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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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