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	12168o	Isogeny class
Conductor	12168	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	1971216 = 24 · 36 · 132	Discriminant
Eigenvalues	2- 3-  2  1  1 13+ -3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-39,-65]	[a1,a2,a3,a4,a6]
Generators	[-3:5:1]	Generators of the group modulo torsion
j	3328	j-invariant
L	5.4709030545806	L(r)(E,1)/r!
Ω	1.9548497031784	Real period
R	1.3993155191638	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24336g1 97344bz1 1352b1 12168d1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 12168o1

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	1	1	+	-3	-7	-1	-3	-8	1	11	11	12	6	-9	-9	3	-5	2	-12	-4	-1	1

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Quadratic twists for elliptic curve 12168o1

-4	8	-3	13
24336g1	97344bz1	1352b1	12168d1

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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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