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	16576i	Isogeny class
Conductor	16576	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-123094171648 = -1 · 218 · 73 · 372	Discriminant
Eigenvalues	2-  0 -4 7+  4 -4  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-332,17040]	[a1,a2,a3,a4,a6]
Generators	[2:128:1]	Generators of the group modulo torsion
j	-15438249/469567	j-invariant
L	2.8337894582398	L(r)(E,1)/r!
Ω	0.87322776793	Real period
R	1.6225946782232	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	16576g1 4144f1 116032bh1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 16576i1

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	-4	+	4	-4	0	-6	4	6	-2	-	-6	-4	12	-10	-10	8	-4	0	2	-4	0	16	4

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Quadratic twists for elliptic curve 16576i1

-4	8	-7
16576g1	4144f1	116032bh1

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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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