Cremona's table of elliptic curves

6171 = 3 · 11² · 17

Field	Data	Notes
Atkin-Lehner	3- 11- 17-	Signs for the Atkin-Lehner involutions
Class	6171f	Isogeny class
Conductor	6171	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	19200	Modular degree for the optimal curve
Δ	-43652685603483 = -1 · 32 · 1111 · 17	Discriminant
Eigenvalues	0 3- -2 -1 11-  6 17-  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-32589,-2297509]	[a1,a2,a3,a4,a6]
j	-2160697802752/24640803	j-invariant
L	1.4203508482231	L(r)(E,1)/r!
Ω	0.17754385602789	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	98736cn1 18513k1 561b1 104907h1	Quadratic twists by: -4 -3 -11 17

Hecke Eigenvalues for elliptic curve 6171f1

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	-	-2	-1	-	6	-	6	-6	-1	-8	-4	3	-8	9	-1	11	2	11	12	-7	0	16	-5	-16

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Quadratic twists for elliptic curve 6171f1

-4	-3	-11	17
98736cn1	18513k1	561b1	104907h1

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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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