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	2992d	Isogeny class
Conductor	2992	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-813824 = -1 · 28 · 11 · 172	Discriminant
Eigenvalues	2+  1 -1 -2 11-  2 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1,43]	[a1,a2,a3,a4,a6]
Generators	[6:17:1]	Generators of the group modulo torsion
j	-1024/3179	j-invariant
L	3.5272011506109	L(r)(E,1)/r!
Ω	2.2687346834168	Real period
R	0.77734985417044	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	1496e1 11968r1 26928g1 74800i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2992d1

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
+	1	-1	-2	-	2	-	2	1	6	5	-11	0	-10	8	-10	-11	-8	9	-5	-14	4	-2	-9	-13

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Quadratic twists for elliptic curve 2992d1

-4	8	-3	5	-11	17
1496e1	11968r1	26928g1	74800i1	32912d1	50864g1

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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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