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	18096d	Isogeny class
Conductor	18096	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2816	Modular degree for the optimal curve
Δ	-3763968 = -1 · 28 · 3 · 132 · 29	Discriminant
Eigenvalues	2+ 3+  0 -4  0 13+  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,12,-96]	[a1,a2,a3,a4,a6]
Generators	[5:8:1] [20:88:1]	Generators of the group modulo torsion
j	686000/14703	j-invariant
L	5.8316636840954	L(r)(E,1)/r!
Ω	1.207126891963	Real period
R	4.8310278918677	Regulator
r	2	Rank of the group of rational points
S	0.99999999999975	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9048m1 72384dj1 54288d1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 18096d1

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

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Quadratic twists for elliptic curve 18096d1

-4	8	-3
9048m1	72384dj1	54288d1

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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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