Cremona's table of elliptic curves

43296 = 2⁵ · 3 · 11 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 41+	Signs for the Atkin-Lehner involutions
Class	43296z	Isogeny class
Conductor	43296	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	3550272 = 26 · 3 · 11 · 412	Discriminant
Eigenvalues	2- 3-  0  2 11+  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-38,-24]	[a1,a2,a3,a4,a6]
Generators	[-132:224:27]	Generators of the group modulo torsion
j	97336000/55473	j-invariant
L	8.1243391065699	L(r)(E,1)/r!
Ω	2.0753394943255	Real period
R	3.9147036563317	Regulator
r	1	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	43296v1 86592cf1 129888k1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 43296z1

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

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Quadratic twists for elliptic curve 43296z1

-4	8	-3
43296v1	86592cf1	129888k1

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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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