Cremona's table of elliptic curves

11165 = 5 · 7 · 11 · 29

Field	Data	Notes
Atkin-Lehner	5+ 7+ 11+ 29+	Signs for the Atkin-Lehner involutions
Class	11165a	Isogeny class
Conductor	11165	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	20736	Modular degree for the optimal curve
Δ	-12775745018575 = -1 · 52 · 73 · 116 · 292	Discriminant
Eigenvalues	-1  0 5+ 7+ 11+ -4 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-12688,-573158]	[a1,a2,a3,a4,a6]
Generators	[247:3240:1]	Generators of the group modulo torsion
j	-225876542934987729/12775745018575	j-invariant
L	1.8206451329384	L(r)(E,1)/r!
Ω	0.22418172003352	Real period
R	4.0606458293437	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	100485y1 55825j1 78155i1 122815h1	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for elliptic curve 11165a1

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	+	+	+	-4	-2	-2	-4	+	8	-2	2	8	12	-6	10	6	8	12	-6	-16	4	0	-16

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Quadratic twists for elliptic curve 11165a1

-3	5	-7	-11
100485y1	55825j1	78155i1	122815h1

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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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