Cremona's table of elliptic curves

1281 = 3 · 7 · 61

Field	Data	Notes
Atkin-Lehner	3- 7+ 61+	Signs for the Atkin-Lehner involutions
Class	1281c	Isogeny class
Conductor	1281	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	6480	Modular degree for the optimal curve
Δ	-5702096824455969 = -1 · 39 · 73 · 615	Discriminant
Eigenvalues	-1 3-  3 7+  4 -2  4 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-16289,-3721518]	[a1,a2,a3,a4,a6]
j	-477978815192585617/5702096824455969	j-invariant
L	1.6382472179335	L(r)(E,1)/r!
Ω	0.18202746865927	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	20496p1 81984j1 3843d1 32025h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1281c1

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	+	4	-2	4	-1	0	3	0	-4	2	1	10	-9	-3	+	-1	10	4	9	-2	-4	-2

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Quadratic twists for elliptic curve 1281c1

-4	8	-3	5	-7	61
20496p1	81984j1	3843d1	32025h1	8967e1	78141i1

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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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