Cremona's table of elliptic curves

12144 = 2⁴ · 3 · 11 · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 23-	Signs for the Atkin-Lehner involutions
Class	12144bo	Isogeny class
Conductor	12144	Conductor
∏ cp	420	Product of Tamagawa factors cp
deg	1310400	Modular degree for the optimal curve
Δ	-3.6951244754477E+22	Discriminant
Eigenvalues	2- 3-  2 -3 11-  1  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-50952032,-140310023052]	[a1,a2,a3,a4,a6]
Generators	[12922:1165824:1]	Generators of the group modulo torsion
j	-3571480626044740843224673/9021299988885921792	j-invariant
L	5.9337659983639	L(r)(E,1)/r!
Ω	0.028249675685653	Real period
R	0.50011244160917	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	1518k1 48576cg1 36432bl1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 12144bo1

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	-3	-	1	2	-4	-	-8	-7	-1	1	10	-2	2	-5	14	-11	12	-6	4	-11	-18	-14

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Quadratic twists for elliptic curve 12144bo1

-4	8	-3
1518k1	48576cg1	36432bl1

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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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