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	12144u	Isogeny class
Conductor	12144	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	14976	Modular degree for the optimal curve
Δ	-35904719664 = -1 · 24 · 36 · 11 · 234	Discriminant
Eigenvalues	2- 3+  2 -2 11+  6  4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4757,-125040]	[a1,a2,a3,a4,a6]
Generators	[1129490:37870443:1000]	Generators of the group modulo torsion
j	-744208243621888/2244044979	j-invariant
L	4.4080762190207	L(r)(E,1)/r!
Ω	0.28737583098959	Real period
R	7.6695319224329	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3036g1 48576dy1 36432cf1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 12144u1

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

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Quadratic twists for elliptic curve 12144u1

-4	8	-3
3036g1	48576dy1	36432cf1

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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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