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	12166g	Isogeny class
Conductor	12166	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-21651976192 = -1 · 212 · 7 · 112 · 792	Discriminant
Eigenvalues	2+ -2  2 7+ 11- -4 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,675,-2056]	[a1,a2,a3,a4,a6]
Generators	[28:183:1]	Generators of the group modulo torsion
j	34084708870967/21651976192	j-invariant
L	2.2537462835396	L(r)(E,1)/r!
Ω	0.69366218329549	Real period
R	1.6245272827418	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	97328z1 109494bl1 85162s1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12166g1

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

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Quadratic twists for elliptic curve 12166g1

-4	-3	-7
97328z1	109494bl1	85162s1

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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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