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	8	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	608740352 = 210 · 112 · 173	Discriminant
Eigenvalues	2+  0  0  2 11-  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-198155,33951242]	[a1,a2,a3,a4,a6]
j	840308702533978500/594473	j-invariant
L	2.0151220417927	L(r)(E,1)/r!
Ω	1.0075610208963	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	1496a1 11968m1 26928k1 74800n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2992b1

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 2992b1

-4	8	-3	5	-11	17
1496a1	11968m1	26928k1	74800n1	32912h1	50864a1

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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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