Cremona's table of elliptic curves

2992 = 2⁴ · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 11+ 17+	Signs for the Atkin-Lehner involutions
Class	2992f	Isogeny class
Conductor	2992	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-1087542308864 = -1 · 212 · 11 · 176	Discriminant
Eigenvalues	2- -1  3 -2 11+  2 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1589,56317]	[a1,a2,a3,a4,a6]
j	-108394872832/265513259	j-invariant
L	1.5433886113147	L(r)(E,1)/r!
Ω	0.77169430565734	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	187a2 11968u2 26928bz2 74800bk2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2992f2

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	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 2992f2

-4	8	-3	5	-11	17
187a2	11968u2	26928bz2	74800bk2	32912z2	50864bn2

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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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