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	128	Product of Tamagawa factors cp
Δ	-1721250000000000000 = -1 · 213 · 34 · 516 · 17	Discriminant
Eigenvalues	2- 3- 5-  0 -4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,104800,61791348]	[a1,a2,a3,a4,a6]
Generators	[-209:5550:1]	Generators of the group modulo torsion
j	31077313442863199/420227050781250	j-invariant
L	4.3836261716152	L(r)(E,1)/r!
Ω	0.19654171091459	Real period
R	2.7879744655832	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	510e8 16320bt8 12240bm8 20400bt8	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4080be8

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 4080be8

-4	8	-3	5	17
510e8	16320bt8	12240bm8	20400bt8	69360cb7

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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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