Cremona's table of elliptic curves

12168 = 2³ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13-	Signs for the Atkin-Lehner involutions
Class	12168x	Isogeny class
Conductor	12168	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	168130926288 = 24 · 314 · 133	Discriminant
Eigenvalues	2- 3-  4 -2 -2 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3198,-66755]	[a1,a2,a3,a4,a6]
j	141150208/6561	j-invariant
L	2.5467625581599	L(r)(E,1)/r!
Ω	0.63669063953998	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24336w1 97344dp1 4056j1 12168k1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 12168x1

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

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Quadratic twists for elliptic curve 12168x1

-4	8	-3	13
24336w1	97344dp1	4056j1	12168k1

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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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