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	4080bf	Isogeny class
Conductor	4080	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-2974320 = -1 · 24 · 37 · 5 · 17	Discriminant
Eigenvalues	2- 3- 5- -3 -1 -2 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,30,-45]	[a1,a2,a3,a4,a6]
Generators	[3:9:1]	Generators of the group modulo torsion
j	180472064/185895	j-invariant
L	4.1688286881345	L(r)(E,1)/r!
Ω	1.3762689836876	Real period
R	0.43272569716136	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1020d1 16320bv1 12240bp1 20400bx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4080bf1

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
-	-	-	-3	-1	-2	-	-1	-6	7	10	-3	-9	-8	-3	5	-8	10	-16	-12	-9	-2	-12	0	-2

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Quadratic twists for elliptic curve 4080bf1

-4	8	-3	5	17
1020d1	16320bv1	12240bp1	20400bx1	69360ce1

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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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