Cremona's table of elliptic curves

8041 = 11 · 17 · 43

Field	Data	Notes
Atkin-Lehner	11- 17- 43+	Signs for the Atkin-Lehner involutions
Class	8041b	Isogeny class
Conductor	8041	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	9144	Modular degree for the optimal curve
Δ	-12090986347 = -1 · 113 · 173 · 432	Discriminant
Eigenvalues	-2 -2  2  3 11- -2 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1072,-14872]	[a1,a2,a3,a4,a6]
Generators	[254:4020:1]	Generators of the group modulo torsion
j	-136368207106048/12090986347	j-invariant
L	1.8172230299748	L(r)(E,1)/r!
Ω	0.41504619790032	Real period
R	0.24324240412111	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	128656r1 72369i1 88451c1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 8041b1

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
-2	-2	2	3	-	-2	-	-8	-4	-3	8	6	11	+	-5	1	-3	2	-9	2	-7	4	0	11	-8

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Quadratic twists for elliptic curve 8041b1

-4	-3	-11
128656r1	72369i1	88451c1

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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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