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	6171a	Isogeny class
Conductor	6171	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	38400	Modular degree for the optimal curve
Δ	-19561865326443 = -1 · 310 · 117 · 17	Discriminant
Eigenvalues	0 3+ -2  3 11- -2 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-451249,116824311]	[a1,a2,a3,a4,a6]
Generators	[763:14701:1]	Generators of the group modulo torsion
j	-5736108018368512/11042163	j-invariant
L	2.5231854772658	L(r)(E,1)/r!
Ω	0.58833768511209	Real period
R	0.53608360069291	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	98736dn1 18513l1 561a1 104907bb1	Quadratic twists by: -4 -3 -11 17

Hecke Eigenvalues for elliptic curve 6171a1

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	3	-	-2	-	-2	2	-9	8	-12	3	0	5	11	7	2	3	-4	13	-8	-16	15	16

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Quadratic twists for elliptic curve 6171a1

-4	-3	-11	17
98736dn1	18513l1	561a1	104907bb1

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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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