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	17600r	Isogeny class
Conductor	17600	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	141724880000000 = 210 · 57 · 116	Discriminant
Eigenvalues	2+ -2 5+  4 11- -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-44533,-3586437]	[a1,a2,a3,a4,a6]
j	610462990336/8857805	j-invariant
L	1.9736090226092	L(r)(E,1)/r!
Ω	0.32893483710153	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17600bv3 1100b3 3520g3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 17600r3

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	+	4	-	-4	0	4	6	6	8	2	6	8	-6	-6	12	-2	-10	-12	16	8	0	6	-14

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Quadratic twists for elliptic curve 17600r3

-4	8	5
17600bv3	1100b3	3520g3

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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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