Cremona's table of elliptic curves

41328 = 2⁴ · 3² · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 41-	Signs for the Atkin-Lehner involutions
Class	41328bo	Isogeny class
Conductor	41328	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	177191219810304 = 212 · 37 · 7 · 414	Discriminant
Eigenvalues	2- 3- -2 7+  0  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-21171,997810]	[a1,a2,a3,a4,a6]
j	351447414193/59340981	j-invariant
L	2.1777317294632	L(r)(E,1)/r!
Ω	0.54443293234738	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2583e3 13776o3	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 41328bo3

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

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Quadratic twists for elliptic curve 41328bo3

-4	-3
2583e3	13776o3

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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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