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	1166c	Isogeny class
Conductor	1166	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-6009134912 = -1 · 26 · 116 · 53	Discriminant
Eigenvalues	2+  1  0  2 11-  5  3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-316,4282]	[a1,a2,a3,a4,a6]
j	-3473824173625/6009134912	j-invariant
L	1.6039847211244	L(r)(E,1)/r!
Ω	1.2029885408433	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	9328g1 37312h1 10494d1 29150p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1166c1

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	-	5	3	-7	9	-3	8	11	0	8	0	+	-12	8	-4	-9	8	11	9	-6	5

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Quadratic twists for elliptic curve 1166c1

-4	8	-3	5	-7	-11	53
9328g1	37312h1	10494d1	29150p1	57134n1	12826g1	61798h1

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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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