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	32	Product of Tamagawa factors cp
Δ	33211047168 = 28 · 310 · 133	Discriminant
Eigenvalues	2- 3-  4 -2 -2 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-50583,-4378790]	[a1,a2,a3,a4,a6]
j	34909201168/81	j-invariant
L	2.5467625581599	L(r)(E,1)/r!
Ω	0.31834531976999	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	24336w2 97344dp2 4056j2 12168k2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 12168x2

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 12168x2

-4	8	-3	13
24336w2	97344dp2	4056j2	12168k2

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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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