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	2992b	Isogeny class
Conductor	2992	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-723759406548992 = -1 · 211 · 114 · 176	Discriminant
Eigenvalues	2+  0  0  2 11-  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-198115,33965634]	[a1,a2,a3,a4,a6]
j	-419899962807227250/353398147729	j-invariant
L	2.0151220417927	L(r)(E,1)/r!
Ω	0.50378051044817	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1496a2 11968m2 26928k2 74800n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2992b2

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	2	-	6	+	-4	2	4	10	-4	-2	12	8	2	4	-8	-4	6	-14	-2	-4	6	14

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Quadratic twists for elliptic curve 2992b2

-4	8	-3	5	-11	17
1496a2	11968m2	26928k2	74800n2	32912h2	50864a2

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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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