Cremona's table of elliptic curves

4080 = 2⁴ · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 17-	Signs for the Atkin-Lehner involutions
Class	4080be	Isogeny class
Conductor	4080	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	16711680 = 216 · 3 · 5 · 17	Discriminant
Eigenvalues	2- 3- 5-  0 -4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-348160,-79187020]	[a1,a2,a3,a4,a6]
Generators	[370909:9761928:343]	Generators of the group modulo torsion
j	1139466686381936641/4080	j-invariant
L	4.3836261716152	L(r)(E,1)/r!
Ω	0.19654171091459	Real period
R	11.151897862333	Regulator
r	1	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	510e4 16320bt3 12240bm4 20400bt3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4080be3

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

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Quadratic twists for elliptic curve 4080be3

-4	8	-3	5	17
510e4	16320bt3	12240bm4	20400bt3	69360cb4

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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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