Cremona's table of elliptic curves

1584 = 2⁴ · 3² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 11+	Signs for the Atkin-Lehner involutions
Class	1584n	Isogeny class
Conductor	1584	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	1576599552 = 216 · 37 · 11	Discriminant
Eigenvalues	2- 3- -2  4 11+ -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-291,34]	[a1,a2,a3,a4,a6]
Generators	[-15:32:1]	Generators of the group modulo torsion
j	912673/528	j-invariant
L	2.7345658760368	L(r)(E,1)/r!
Ω	1.272702307929	Real period
R	1.0743148099129	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	198a1 6336ci1 528j1 39600do1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584n1

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

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Quadratic twists for elliptic curve 1584n1

-4	8	-3	5	-7	-11
198a1	6336ci1	528j1	39600do1	77616fh1	17424bz1

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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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