Cremona's table of elliptic curves

106722 = 2 · 3² · 7² · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	106722i	Isogeny class
Conductor	106722	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	806400	Modular degree for the optimal curve
Δ	-12132683589740868 = -1 · 22 · 33 · 78 · 117	Discriminant
Eigenvalues	2+ 3+ -2 7+ 11- -2  3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,7782,5290984]	[a1,a2,a3,a4,a6]
Generators	[674:17450:1] [-10:2288:1]	Generators of the group modulo torsion
j	189/44	j-invariant
L	7.5937373377447	L(r)(E,1)/r!
Ω	0.31022618898093	Real period
R	0.5099597222088	Regulator
r	2	Rank of the group of rational points
S	1.000000000306	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	106722eg1 106722x1 9702bb1	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 106722i1

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	+	-	-2	3	-7	-7	5	2	3	-6	-11	-7	-4	11	-10	-4	-5	8	8	-14	2	15

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Quadratic twists for elliptic curve 106722i1

-3	-7	-11
106722eg1	106722x1	9702bb1

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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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