Cremona's table of elliptic curves

1166 = 2 · 11 · 53

Field	Data	Notes
Atkin-Lehner	2+ 11+ 53+	Signs for the Atkin-Lehner involutions
Class	1166a	Isogeny class
Conductor	1166	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-25652 = -1 · 22 · 112 · 53	Discriminant
Eigenvalues	2+  1  0 -2 11+  1  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1,-8]	[a1,a2,a3,a4,a6]
Generators	[5:8:1]	Generators of the group modulo torsion
j	-15625/25652	j-invariant
L	2.1443854086046	L(r)(E,1)/r!
Ω	1.7044195544787	Real period
R	0.31453309177453	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	9328l1 37312r1 10494f1 29150n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1166a1

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	0	-2	+	1	3	1	-3	1	0	-9	-12	-4	4	+	8	-8	-12	-5	16	-1	9	-14	5

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Quadratic twists for elliptic curve 1166a1

-4	8	-3	5	-7	-11	53
9328l1	37312r1	10494f1	29150n1	57134c1	12826f1	61798f1

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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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