Cremona's table of elliptic curves

8040 = 2³ · 3 · 5 · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 67+	Signs for the Atkin-Lehner involutions
Class	8040k	Isogeny class
Conductor	8040	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2176	Modular degree for the optimal curve
Δ	-55572480 = -1 · 211 · 34 · 5 · 67	Discriminant
Eigenvalues	2- 3- 5- -1  3  2 -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-80,-480]	[a1,a2,a3,a4,a6]
j	-27995042/27135	j-invariant
L	3.0683475253362	L(r)(E,1)/r!
Ω	0.76708688133405	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16080e1 64320d1 24120e1 40200e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8040k1

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
-	-	-	-1	3	2	-2	6	-8	-4	8	1	2	-6	-2	12	6	13	+	9	16	14	-9	-3	-5

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Quadratic twists for elliptic curve 8040k1

-4	8	-3	5
16080e1	64320d1	24120e1	40200e1

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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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