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	12144p	Isogeny class
Conductor	12144	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	253440	Modular degree for the optimal curve
Δ	1331440775086473216 = 223 · 34 · 115 · 233	Discriminant
Eigenvalues	2- 3+ -1  5 11+ -5  1  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-347776,-56004608]	[a1,a2,a3,a4,a6]
j	1135700552684700289/325058782980096	j-invariant
L	1.6070509554083	L(r)(E,1)/r!
Ω	0.20088136942603	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1518t1 48576dn1 36432cr1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 12144p1

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
-	+	-1	5	+	-5	1	6	+	-5	-7	-11	8	2	11	-2	0	-2	-3	-5	0	5	14	4	16

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Quadratic twists for elliptic curve 12144p1

-4	8	-3
1518t1	48576dn1	36432cr1

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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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