Cremona's table of elliptic curves

17600 = 2⁶ · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	17600d	Isogeny class
Conductor	17600	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	-3489136640000000 = -1 · 225 · 57 · 113	Discriminant
Eigenvalues	2+  1 5+ -5 11+  2 -3  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-141633,20664863]	[a1,a2,a3,a4,a6]
Generators	[-197:6400:1]	Generators of the group modulo torsion
j	-76711450249/851840	j-invariant
L	4.6354892294261	L(r)(E,1)/r!
Ω	0.44685732930841	Real period
R	1.296691618721	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	17600cj1 550i1 3520j1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 17600d1

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

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Quadratic twists for elliptic curve 17600d1

-4	8	5
17600cj1	550i1	3520j1

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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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