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	12168f	Isogeny class
Conductor	12168	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	12331029336148224 = 28 · 310 · 138	Discriminant
Eigenvalues	2+ 3- -2 -4  0 13+ -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-67431,-4108390]	[a1,a2,a3,a4,a6]
Generators	[-146:1620:1] [-77:792:1]	Generators of the group modulo torsion
j	37642192/13689	j-invariant
L	5.4490450791894	L(r)(E,1)/r!
Ω	0.30527013066763	Real period
R	8.9249561810611	Regulator
r	2	Rank of the group of rational points
S	0.99999999999975	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	24336l2 97344bx2 4056m2 936i2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 12168f2

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

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Quadratic twists for elliptic curve 12168f2

-4	8	-3	13
24336l2	97344bx2	4056m2	936i2

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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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