Cremona's table of elliptic curves

5841 = 3² · 11 · 59

Field	Data	Notes
Atkin-Lehner	3- 11- 59+	Signs for the Atkin-Lehner involutions
Class	5841i	Isogeny class
Conductor	5841	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	4258089 = 38 · 11 · 59	Discriminant
Eigenvalues	-1 3- -2  2 11- -2  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-131,-534]	[a1,a2,a3,a4,a6]
Generators	[-6:5:1]	Generators of the group modulo torsion
j	338608873/5841	j-invariant
L	2.2937850882735	L(r)(E,1)/r!
Ω	1.4134990697123	Real period
R	1.6227708510204	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	93456bi1 1947a1 64251o1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 5841i1

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	-	-2	2	-	-2	0	6	-4	-4	2	2	0	-4	-4	-6	+	2	10	8	6	14	4	-12	14

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Quadratic twists for elliptic curve 5841i1

-4	-3	-11
93456bi1	1947a1	64251o1

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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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