Cremona's table of elliptic curves

13600 = 2⁵ · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 5+ 17-	Signs for the Atkin-Lehner involutions
Class	13600d	Isogeny class
Conductor	13600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	-680000000000 = -1 · 212 · 510 · 17	Discriminant
Eigenvalues	2+ -1 5+ -3  0  5 17-  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-833,-40463]	[a1,a2,a3,a4,a6]
j	-1600/17	j-invariant
L	1.5412086837895	L(r)(E,1)/r!
Ω	0.38530217094737	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13600t1 27200w1 122400de1 13600v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13600d1

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	+	-3	0	5	-	8	8	2	3	2	-12	-10	-2	9	14	6	4	-7	-2	11	0	-14	0

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Quadratic twists for elliptic curve 13600d1

-4	8	-3	5
13600t1	27200w1	122400de1	13600v1

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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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