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	4080v	Isogeny class
Conductor	4080	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-255688704000 = -1 · 218 · 33 · 53 · 172	Discriminant
Eigenvalues	2- 3+ 5- -2  0 -4 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,400,24000]	[a1,a2,a3,a4,a6]
Generators	[10:170:1]	Generators of the group modulo torsion
j	1723683599/62424000	j-invariant
L	3.0669240261171	L(r)(E,1)/r!
Ω	0.74338083839735	Real period
R	0.68760718322368	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	510g1 16320cl1 12240bs1 20400dl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4080v1

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	0	6	4	2	0	-2	0	-6	-6	-10	-2	6	-16	-8	0	6	-4

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Quadratic twists for elliptic curve 4080v1

-4	8	-3	5	17
510g1	16320cl1	12240bs1	20400dl1	69360db1

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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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