Cremona's table of elliptic curves

16576 = 2⁶ · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 7+ 37-	Signs for the Atkin-Lehner involutions
Class	16576k	Isogeny class
Conductor	16576	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	119040	Modular degree for the optimal curve
Δ	-22692544 = -1 · 26 · 7 · 373	Discriminant
Eigenvalues	2-  2  3 7+ -5  7 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-832459,-292065483]	[a1,a2,a3,a4,a6]
Generators	[11248241569644680491044:585775931979182631461007:3723810132876649271]	Generators of the group modulo torsion
j	-996856898790659465728/354571	j-invariant
L	8.1258035914899	L(r)(E,1)/r!
Ω	0.079027601693138	Real period
R	34.274116120602	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	16576v1 8288d1 116032bw1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 16576k1

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	3	+	-5	7	-2	0	-4	-8	-1	-	-4	-4	-8	-1	-1	-10	-1	-3	12	2	-14	-3	7

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Quadratic twists for elliptic curve 16576k1

-4	8	-7
16576v1	8288d1	116032bw1

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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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