Cremona's table of elliptic curves

11661 = 3 · 13² · 23

Field	Data	Notes
Atkin-Lehner	3- 13+ 23+	Signs for the Atkin-Lehner involutions
Class	11661i	Isogeny class
Conductor	11661	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	6168669 = 3 · 132 · 233	Discriminant
Eigenvalues	0 3- -3 -2 -3 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-407,-3298]	[a1,a2,a3,a4,a6]
Generators	[-12:1:1] [42:235:1]	Generators of the group modulo torsion
j	44226936832/36501	j-invariant
L	5.2494923726334	L(r)(E,1)/r!
Ω	1.0627560447269	Real period
R	4.9395083647661	Regulator
r	2	Rank of the group of rational points
S	0.99999999999981	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34983f2 11661h2	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 11661i2

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
0	-	-3	-2	-3	+	-3	-2	+	0	-8	-2	-6	-4	0	-3	-6	-4	4	-12	-14	-10	-3	-3	10

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Quadratic twists for elliptic curve 11661i2

-3	13
34983f2	11661h2

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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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