Cremona's table of elliptic curves

27200 = 2⁶ · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 5+ 17+	Signs for the Atkin-Lehner involutions
Class	27200c	Isogeny class
Conductor	27200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	16384	Modular degree for the optimal curve
Δ	69632000000 = 218 · 56 · 17	Discriminant
Eigenvalues	2+  0 5+ -4  0 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1100,6000]	[a1,a2,a3,a4,a6]
Generators	[-34:64:1]	Generators of the group modulo torsion
j	35937/17	j-invariant
L	3.6361711461449	L(r)(E,1)/r!
Ω	0.9784591486307	Real period
R	1.858110863	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	27200br1 425a1 1088e1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 27200c1

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

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Quadratic twists for elliptic curve 27200c1

-4	8	5
27200br1	425a1	1088e1

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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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