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	1065c	Isogeny class
Conductor	1065	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-258795 = -1 · 36 · 5 · 71	Discriminant
Eigenvalues	0 3+ 5-  1 -2 -1 -2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-25,63]	[a1,a2,a3,a4,a6]
Generators	[7:13:1]	Generators of the group modulo torsion
j	-1798045696/258795	j-invariant
L	1.9997952210375	L(r)(E,1)/r!
Ω	3.0054448904475	Real period
R	0.33269537355246	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17040y1 68160bc1 3195a1 5325k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1065c1

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
0	+	-	1	-2	-1	-2	-1	0	7	-8	8	-12	-12	-1	-7	-6	0	-8	-	-6	11	-16	-15	15

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Quadratic twists for elliptic curve 1065c1

-4	8	-3	5	-7	-11	-71
17040y1	68160bc1	3195a1	5325k1	52185j1	128865k1	75615d1

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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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