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	17600cw	Isogeny class
Conductor	17600	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	468512000000000 = 214 · 59 · 114	Discriminant
Eigenvalues	2- -2 5- -2 11+  0 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-22833,816463]	[a1,a2,a3,a4,a6]
Generators	[-46:1331:1]	Generators of the group modulo torsion
j	41141648/14641	j-invariant
L	2.7219148805095	L(r)(E,1)/r!
Ω	0.48236914494915	Real period
R	2.8214023523379	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	17600bg2 4400j2 17600cv2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 17600cw2

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

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Quadratic twists for elliptic curve 17600cw2

-4	8	5
17600bg2	4400j2	17600cv2

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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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