Cremona's table of elliptic curves

1065 = 3 · 5 · 71

Field	Data	Notes
Atkin-Lehner	3+ 5- 71+	Signs for the Atkin-Lehner involutions
Class	1065b	Isogeny class
Conductor	1065	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-399375 = -1 · 32 · 54 · 71	Discriminant
Eigenvalues	-1 3+ 5-  4  4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,5,32]	[a1,a2,a3,a4,a6]
j	13651919/399375	j-invariant
L	1.1282339944332	L(r)(E,1)/r!
Ω	2.2564679888665	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17040bd1 68160z1 3195c1 5325j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1065b1

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

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Quadratic twists for elliptic curve 1065b1

-4	8	-3	5	-7	-11	-71
17040bd1	68160z1	3195c1	5325j1	52185i1	128865i1	75615f1

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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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