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	1584f	Isogeny class
Conductor	1584	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	24634368 = 210 · 37 · 11	Discriminant
Eigenvalues	2+ 3-  0 -2 11-  0  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-75,74]	[a1,a2,a3,a4,a6]
Generators	[-5:18:1]	Generators of the group modulo torsion
j	62500/33	j-invariant
L	2.740340604523	L(r)(E,1)/r!
Ω	1.8652305447207	Real period
R	0.36729247924327	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	792b1 6336bv1 528a1 39600ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584f1

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

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Quadratic twists for elliptic curve 1584f1

-4	8	-3	5	-7	-11
792b1	6336bv1	528a1	39600ba1	77616cb1	17424q1

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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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