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	106722gq	Isogeny class
Conductor	106722	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	221184	Modular degree for the optimal curve
Δ	-3362375007684 = -1 · 22 · 310 · 76 · 112	Discriminant
Eigenvalues	2- 3- -1 7- 11- -5 -7  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5963,199455]	[a1,a2,a3,a4,a6]
Generators	[107:828:1]	Generators of the group modulo torsion
j	-2259169/324	j-invariant
L	8.357394465826	L(r)(E,1)/r!
Ω	0.76761101967896	Real period
R	1.3609422919524	Regulator
r	1	Rank of the group of rational points
S	1.0000000074458	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	35574l1 2178j1 106722db1	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 106722gq1

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	-	-	-5	-7	0	0	7	8	-5	-11	8	4	5	0	-2	12	16	-6	-4	8	-17	5

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Quadratic twists for elliptic curve 106722gq1

-3	-7	-11
35574l1	2178j1	106722db1

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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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