Cremona's table of elliptic curves

8540 = 2² · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 61-	Signs for the Atkin-Lehner involutions
Class	8540c	Isogeny class
Conductor	8540	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-937350400 = -1 · 28 · 52 · 74 · 61	Discriminant
Eigenvalues	2- -2 5+ 7+  4 -6  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,244,244]	[a1,a2,a3,a4,a6]
Generators	[19:110:1]	Generators of the group modulo torsion
j	6249886256/3661525	j-invariant
L	2.4577100475056	L(r)(E,1)/r!
Ω	0.95145333631344	Real period
R	2.5831114923916	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	34160w2 76860j2 42700j2 59780k2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8540c2

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	+	+	4	-6	0	0	0	10	-8	-4	-6	8	-2	-8	-4	-	8	0	14	16	6	10	-6

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Quadratic twists for elliptic curve 8540c2

-4	-3	5	-7
34160w2	76860j2	42700j2	59780k2

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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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