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	1584o	Isogeny class
Conductor	1584	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-248396544 = -1 · 28 · 36 · 113	Discriminant
Eigenvalues	2- 3-  3 -2 11+ -4 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-696,-7108]	[a1,a2,a3,a4,a6]
Generators	[38:146:1]	Generators of the group modulo torsion
j	-199794688/1331	j-invariant
L	3.0492557716185	L(r)(E,1)/r!
Ω	0.46456275073366	Real period
R	3.2818556446927	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	396c2 6336cm2 176c2 39600de2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584o2

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
-	-	3	-2	+	-4	-6	-8	-3	0	-5	-1	0	10	0	6	3	-4	1	15	-4	-2	6	9	-7

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Quadratic twists for elliptic curve 1584o2

-4	8	-3	5	-7	-11
396c2	6336cm2	176c2	39600de2	77616fr2	17424ca2

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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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