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	17600bv	Isogeny class
Conductor	17600	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	242000000000 = 210 · 59 · 112	Discriminant
Eigenvalues	2-  2 5+ -4 11+ -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4533,-113563]	[a1,a2,a3,a4,a6]
j	643956736/15125	j-invariant
L	1.1653234274185	L(r)(E,1)/r!
Ω	0.58266171370927	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	17600r1 4400t1 3520u1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 17600bv1

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 17600bv1

-4	8	5
17600r1	4400t1	3520u1

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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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