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	12168p	Isogeny class
Conductor	12168	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	49920	Modular degree for the optimal curve
Δ	-456704790227712 = -1 · 28 · 37 · 138	Discriminant
Eigenvalues	2- 3-  2  1  6 13+ -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26364,1942148]	[a1,a2,a3,a4,a6]
Generators	[169:1521:1]	Generators of the group modulo torsion
j	-13312/3	j-invariant
L	5.761913313662	L(r)(E,1)/r!
Ω	0.50353411965025	Real period
R	0.47678938136176	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	24336h1 97344ca1 4056b1 12168e1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 12168p1

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	6	+	-8	-4	-2	-10	7	2	4	-7	-6	0	6	-5	-7	-6	1	1	0	-4	-19

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Quadratic twists for elliptic curve 12168p1

-4	8	-3	13
24336h1	97344ca1	4056b1	12168e1

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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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