Cremona's table of elliptic curves

43320 = 2³ · 3 · 5 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	43320t	Isogeny class
Conductor	43320	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	180656183040000 = 211 · 3 · 54 · 196	Discriminant
Eigenvalues	2- 3+ 5+  4  0  6 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-49216,-4136084]	[a1,a2,a3,a4,a6]
Generators	[-1237522:-239925:10648]	Generators of the group modulo torsion
j	136835858/1875	j-invariant
L	5.83650467745	L(r)(E,1)/r!
Ω	0.3207985786294	Real period
R	9.0968368725087	Regulator
r	1	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	86640u3 129960bk3 120b4	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 43320t3

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
-	+	+	4	0	6	-2	-	-8	6	0	6	-10	-4	8	-10	0	6	4	0	-14	-16	12	-2	-2

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Quadratic twists for elliptic curve 43320t3

-4	-3	-19
86640u3	129960bk3	120b4

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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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