Cremona's table of elliptic curves

3179 = 11 · 17²

Field	Data	Notes
Atkin-Lehner	11+ 17+	Signs for the Atkin-Lehner involutions
Class	3179a	Isogeny class
Conductor	3179	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-6408844609527371 = -1 · 11 · 1712	Discriminant
Eigenvalues	0 -1 -3 -2 11+  2 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-28707,-4272975]	[a1,a2,a3,a4,a6]
Generators	[2394:29763:8]	Generators of the group modulo torsion
j	-108394872832/265513259	j-invariant
L	1.5695347600179	L(r)(E,1)/r!
Ω	0.170958262966	Real period
R	4.5904033323327	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	50864bn2 28611r2 79475a2 34969d2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3179a2

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	-1	-3	-2	+	2	+	2	3	6	7	7	-12	-10	0	6	-3	-8	-7	9	-2	-8	6	15	-11

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Quadratic twists for elliptic curve 3179a2

-4	-3	5	-11	17
50864bn2	28611r2	79475a2	34969d2	187a2

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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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