Cremona's table of elliptic curves

50094 = 2 · 3² · 11² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 11- 23+	Signs for the Atkin-Lehner involutions
Class	50094t	Isogeny class
Conductor	50094	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	161280	Modular degree for the optimal curve
Δ	-125468696124288 = -1 · 27 · 37 · 117 · 23	Discriminant
Eigenvalues	2+ 3- -2 -3 11- -1  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,11412,262224]	[a1,a2,a3,a4,a6]
Generators	[3:543:1]	Generators of the group modulo torsion
j	127263527/97152	j-invariant
L	3.1028436568407	L(r)(E,1)/r!
Ω	0.37606859841249	Real period
R	1.0313423102754	Regulator
r	1	Rank of the group of rational points
S	0.99999999999049	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16698bp1 4554ba1	Quadratic twists by: -3 -11

Hecke Eigenvalues for elliptic curve 50094t1

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	-3	-	-1	6	4	+	4	-5	3	3	2	6	6	-11	2	-13	4	10	-12	-7	-2	-10

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Quadratic twists for elliptic curve 50094t1

-3	-11
16698bp1	4554ba1

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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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