Cremona's table of elliptic curves

11200 = 2⁶ · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 5- 7+	Signs for the Atkin-Lehner involutions
Class	11200cx	Isogeny class
Conductor	11200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-702464000 = -1 · 214 · 53 · 73	Discriminant
Eigenvalues	2- -1 5- 7+ -1 -1  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,27,-1283]	[a1,a2,a3,a4,a6]
Generators	[12:25:1]	Generators of the group modulo torsion
j	1024/343	j-invariant
L	3.2784482283125	L(r)(E,1)/r!
Ω	0.75467410214491	Real period
R	2.1720953581119	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11200bn1 2800j1 100800oj1 11200dd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 11200cx1

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	-1	3	-4	2	1	6	2	-10	0	9	-14	6	4	-10	16	-10	11	-4	12	19

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Quadratic twists for elliptic curve 11200cx1

-4	8	-3	5	-7
11200bn1	2800j1	100800oj1	11200dd1	78400ki1

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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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