Cremona's table of elliptic curves

11600 = 2⁴ · 5² · 29

Field	Data	Notes
Atkin-Lehner	2+ 5+ 29+	Signs for the Atkin-Lehner involutions
Class	11600f	Isogeny class
Conductor	11600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	181250000 = 24 · 58 · 29	Discriminant
Eigenvalues	2+ -2 5+  0 -4  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-283,-1812]	[a1,a2,a3,a4,a6]
Generators	[-8:2:1]	Generators of the group modulo torsion
j	10061824/725	j-invariant
L	2.7411580945915	L(r)(E,1)/r!
Ω	1.1689467916094	Real period
R	2.3449810669462	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	5800h1 46400cb1 104400ba1 2320a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 11600f1

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	+	0	-4	2	0	-4	-4	+	4	8	-2	2	2	14	-4	2	-4	8	12	4	-4	-10	-8

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Quadratic twists for elliptic curve 11600f1

-4	8	-3	5
5800h1	46400cb1	104400ba1	2320a1

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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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