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
deg	1152	Modular degree for the optimal curve
Δ	-1575563264 = -1 · 212 · 113 · 172	Discriminant
Eigenvalues	2- -1  3 -2 11+  2 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,171,-1763]	[a1,a2,a3,a4,a6]
j	134217728/384659	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	187a1 11968u1 26928bz1 74800bk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2992f1

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 2992f1

-4	8	-3	5	-11	17
187a1	11968u1	26928bz1	74800bk1	32912z1	50864bn1

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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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