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	2992h	Isogeny class
Conductor	2992	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-813824 = -1 · 28 · 11 · 172	Discriminant
Eigenvalues	2- -3  3  2 11- -2 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-496,4252]	[a1,a2,a3,a4,a6]
Generators	[18:34:1]	Generators of the group modulo torsion
j	-52714340352/3179	j-invariant
L	2.6756155530613	L(r)(E,1)/r!
Ω	2.676578553106	Real period
R	0.2499100530747	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	748a1 11968o1 26928bm1 74800cn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2992h1

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
-	-3	3	2	-	-2	+	-2	-3	-10	-7	-7	4	-2	0	-10	5	0	9	7	14	-4	-18	-9	-17

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Quadratic twists for elliptic curve 2992h1

-4	8	-3	5	-11	17
748a1	11968o1	26928bm1	74800cn1	32912bc1	50864bh1

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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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