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	2992g	Isogeny class
Conductor	2992	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-554598268928 = -1 · 217 · 114 · 172	Discriminant
Eigenvalues	2-  0  0  2 11- -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2045,4098]	[a1,a2,a3,a4,a6]
Generators	[97:1056:1]	Generators of the group modulo torsion
j	230910510375/135399968	j-invariant
L	3.4205256374789	L(r)(E,1)/r!
Ω	0.55925252888709	Real period
R	0.76453065940661	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	374a2 11968l2 26928bh2 74800ch2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2992g2

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	-	-2	+	4	-6	-4	2	-4	-2	4	0	2	-4	0	-12	-2	2	14	-12	6	-2

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Quadratic twists for elliptic curve 2992g2

-4	8	-3	5	-11	17
374a2	11968l2	26928bh2	74800ch2	32912x2	50864ba2

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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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