Cremona's table of elliptic curves

127050 = 2 · 3 · 5² · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	127050bf	Isogeny class
Conductor	127050	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3317760	Modular degree for the optimal curve
Δ	167412514500000000 = 28 · 33 · 59 · 7 · 116	Discriminant
Eigenvalues	2+ 3+ 5+ 7- 11-  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1505000,-711000000]	[a1,a2,a3,a4,a6]
Generators	[1984:63176:1]	Generators of the group modulo torsion
j	13619385906841/6048000	j-invariant
L	3.5505883906985	L(r)(E,1)/r!
Ω	0.1363097643133	Real period
R	6.5119844840772	Regulator
r	1	Rank of the group of rational points
S	1.0000000309112	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25410ct1 1050k1	Quadratic twists by: 5 -11

Hecke Eigenvalues for elliptic curve 127050bf1

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	-6	-8	0	-6	-4	10	6	-4	0	6	-12	10	4	12	-10	-8	12	-6	10

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Quadratic twists for elliptic curve 127050bf1

5	-11
25410ct1	1050k1

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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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