Cremona's table of elliptic curves

5166 = 2 · 3² · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 41-	Signs for the Atkin-Lehner involutions
Class	5166o	Isogeny class
Conductor	5166	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	69696	Modular degree for the optimal curve
Δ	-127597126080227328 = -1 · 211 · 317 · 7 · 413	Discriminant
Eigenvalues	2+ 3- -4 7+  1  0 -2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,44361,16794589]	[a1,a2,a3,a4,a6]
Generators	[1247:44210:1]	Generators of the group modulo torsion
j	13243252505373071/175030351276032	j-invariant
L	1.966662438223	L(r)(E,1)/r!
Ω	0.24399426597185	Real period
R	0.67169011478938	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41328cn1 1722i1 129150dk1 36162w1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166o1

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	+	1	0	-2	-1	-5	2	9	2	-	-1	9	0	5	-3	-2	-8	4	-15	4	-18	13

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Quadratic twists for elliptic curve 5166o1

-4	-3	5	-7
41328cn1	1722i1	129150dk1	36162w1

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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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