Cremona's table of elliptic curves

18096 = 2⁴ · 3 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 13- 29+	Signs for the Atkin-Lehner involutions
Class	18096u	Isogeny class
Conductor	18096	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1113509256912 = 24 · 32 · 13 · 296	Discriminant
Eigenvalues	2- 3+  0 -2 -6 13-  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-24393,1473660]	[a1,a2,a3,a4,a6]
Generators	[120:510:1]	Generators of the group modulo torsion
j	100326850926592000/69594328557	j-invariant
L	3.2562012732118	L(r)(E,1)/r!
Ω	0.86222183179245	Real period
R	3.776523805298	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	4524e3 72384cw3 54288bv3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 18096u3

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
-	+	0	-2	-6	-	6	-8	0	+	4	8	-6	4	6	6	12	14	-2	12	-16	16	-12	-18	8

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Quadratic twists for elliptic curve 18096u3

-4	8	-3
4524e3	72384cw3	54288bv3

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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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