Cremona's table of elliptic curves

2993 = 41 · 73

Field	Data	Notes
Atkin-Lehner	41- 73-	Signs for the Atkin-Lehner involutions
Class	2993a	Isogeny class
Conductor	2993	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1656	Modular degree for the optimal curve
Δ	-5031233 = -1 · 413 · 73	Discriminant
Eigenvalues	1 -3 -4 -4  4  3 -7 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-4,109]	[a1,a2,a3,a4,a6]
Generators	[12:35:1]	Generators of the group modulo torsion
j	-8120601/5031233	j-invariant
L	1.386451383656	L(r)(E,1)/r!
Ω	1.9643477415454	Real period
R	0.2352691692231	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	47888k1 26937c1 74825b1 122713b1	Quadratic twists by: -4 -3 5 41

Hecke Eigenvalues for elliptic curve 2993a1

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	-3	-4	-4	4	3	-7	-1	4	2	1	-3	-	1	-6	-2	12	7	-16	12	-	5	-11	-6	8

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Quadratic twists for elliptic curve 2993a1

-4	-3	5	41
47888k1	26937c1	74825b1	122713b1

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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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