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	13600o	Isogeny class
Conductor	13600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-1740800 = -1 · 212 · 52 · 17	Discriminant
Eigenvalues	2- -1 5+  1 -4 -7 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-433,3617]	[a1,a2,a3,a4,a6]
Generators	[13:-4:1] [-17:76:1]	Generators of the group modulo torsion
j	-87880000/17	j-invariant
L	5.5564928304036	L(r)(E,1)/r!
Ω	2.5743882123836	Real period
R	0.53959352397539	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13600m1 27200bt1 122400bb1 13600j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13600o1

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	+	1	-4	-7	+	-6	-8	0	7	8	-6	-4	-6	-3	-12	-14	-8	9	-4	-5	-4	-6	8

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Quadratic twists for elliptic curve 13600o1

-4	8	-3	5
13600m1	27200bt1	122400bb1	13600j1

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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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