Cremona's table of elliptic curves

12166 = 2 · 7 · 11 · 79

Field	Data	Notes
Atkin-Lehner	2- 7- 11+ 79+	Signs for the Atkin-Lehner involutions
Class	12166o	Isogeny class
Conductor	12166	Conductor
∏ cp	180	Product of Tamagawa factors cp
Δ	167281607438392832 = 29 · 710 · 114 · 79	Discriminant
Eigenvalues	2- -2 -4 7- 11+  0  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-173355,-19625039]	[a1,a2,a3,a4,a6]
Generators	[1358:-48111:1]	Generators of the group modulo torsion
j	576146576605005871921/167281607438392832	j-invariant
L	3.4026277256152	L(r)(E,1)/r!
Ω	0.23916977870268	Real period
R	0.31615177247003	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97328w2 109494x2 85162y2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12166o2

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	-4	-	+	0	0	4	-4	-2	-2	-10	-8	-8	12	-6	14	10	12	0	6	+	8	-2	10

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Quadratic twists for elliptic curve 12166o2

-4	-3	-7
97328w2	109494x2	85162y2

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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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