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	2992c	Isogeny class
Conductor	2992	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-47872 = -1 · 28 · 11 · 17	Discriminant
Eigenvalues	2+  0  0 -3 11- -4 17+  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-20,-36]	[a1,a2,a3,a4,a6]
j	-3456000/187	j-invariant
L	1.1252475057535	L(r)(E,1)/r!
Ω	1.1252475057535	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	1496b1 11968n1 26928l1 74800o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2992c1

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	0	-3	-	-4	+	6	2	-1	0	6	3	2	3	-3	9	2	11	-14	11	8	6	1	-6

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Quadratic twists for elliptic curve 2992c1

-4	8	-3	5	-11	17
1496b1	11968n1	26928l1	74800o1	32912i1	50864b1

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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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