Cremona's table of elliptic curves

1656 = 2³ · 3² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 23+	Signs for the Atkin-Lehner involutions
Class	1656d	Isogeny class
Conductor	1656	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3584	Modular degree for the optimal curve
Δ	-20530186553088 = -1 · 28 · 320 · 23	Discriminant
Eigenvalues	2- 3-  0 -2  0  2 -8  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26175,-1644478]	[a1,a2,a3,a4,a6]
Generators	[193:702:1]	Generators of the group modulo torsion
j	-10627137250000/110008287	j-invariant
L	2.7705785215064	L(r)(E,1)/r!
Ω	0.18755554012995	Real period
R	3.6930107737509	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	3312d1 13248d1 552b1 41400l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1656d1

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

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Quadratic twists for elliptic curve 1656d1

-4	8	-3	5	-7	-23
3312d1	13248d1	552b1	41400l1	81144bj1	38088q1

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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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