Cremona's table of elliptic curves

120384 = 2⁶ · 3² · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 19+	Signs for the Atkin-Lehner involutions
Class	120384cs	Isogeny class
Conductor	120384	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	229376	Modular degree for the optimal curve
Δ	89866174464 = 216 · 38 · 11 · 19	Discriminant
Eigenvalues	2- 3- -2  2 11+ -6  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-22476,-1296880]	[a1,a2,a3,a4,a6]
Generators	[4514:102969:8]	Generators of the group modulo torsion
j	26282902468/1881	j-invariant
L	5.276266945372	L(r)(E,1)/r!
Ω	0.38991654514099	Real period
R	6.7658926366526	Regulator
r	1	Rank of the group of rational points
S	0.99999999659136	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	120384bx1 30096j1 40128bn1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 120384cs1

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

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Quadratic twists for elliptic curve 120384cs1

-4	8	-3
120384bx1	30096j1	40128bn1

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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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