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	4080z	Isogeny class
Conductor	4080	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-5752995840 = -1 · 214 · 35 · 5 · 172	Discriminant
Eigenvalues	2- 3- 5+ -2  0  4 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,224,-3340]	[a1,a2,a3,a4,a6]
Generators	[26:144:1]	Generators of the group modulo torsion
j	302111711/1404540	j-invariant
L	3.9237691940866	L(r)(E,1)/r!
Ω	0.68069774736176	Real period
R	0.57643340370881	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	510c1 16320cc1 12240ch1 20400cg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4080z1

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

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Quadratic twists for elliptic curve 4080z1

-4	8	-3	5	17
510c1	16320cc1	12240ch1	20400cg1	69360cs1

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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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