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	4080t	Isogeny class
Conductor	4080	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-16711680 = -1 · 216 · 3 · 5 · 17	Discriminant
Eigenvalues	2- 3+ 5+  0 -4  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,64,0]	[a1,a2,a3,a4,a6]
Generators	[1:8:1]	Generators of the group modulo torsion
j	6967871/4080	j-invariant
L	2.8397960396663	L(r)(E,1)/r!
Ω	1.3304186639693	Real period
R	2.1345130796601	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	510f1 16320cz1 12240bw1 20400cy1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4080t1

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

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Quadratic twists for elliptic curve 4080t1

-4	8	-3	5	17
510f1	16320cz1	12240bw1	20400cy1	69360do1

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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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