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	1065a	Isogeny class
Conductor	1065	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-143775 = -1 · 34 · 52 · 71	Discriminant
Eigenvalues	1 3+ 5+ -2  0  0  4  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-13,-32]	[a1,a2,a3,a4,a6]
j	-273359449/143775	j-invariant
L	1.214847919704	L(r)(E,1)/r!
Ω	1.214847919704	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17040s1 68160bo1 3195d1 5325n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1065a1

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

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Quadratic twists for elliptic curve 1065a1

-4	8	-3	5	-7	-11	-71
17040s1	68160bo1	3195d1	5325n1	52185m1	128865e1	75615a1

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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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