Cremona's table of elliptic curves

1085 = 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	5- 7+ 31-	Signs for the Atkin-Lehner involutions
Class	1085h	Isogeny class
Conductor	1085	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-25751796875 = -1 · 57 · 73 · 312	Discriminant
Eigenvalues	-2 -1 5- 7+ -1  3  5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-33290,2349006]	[a1,a2,a3,a4,a6]
Generators	[110:-78:1]	Generators of the group modulo torsion
j	-4080168919667961856/25751796875	j-invariant
L	1.1834518154191	L(r)(E,1)/r!
Ω	1.0620935755536	Real period
R	0.079590230536774	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	17360bi1 69440i1 9765g1 5425h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1085h1

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	-1	-	+	-1	3	5	-2	-8	-3	-	2	0	-6	13	6	-2	-2	-4	-12	-10	-15	4	-8	-9

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Quadratic twists for elliptic curve 1085h1

-4	8	-3	5	-7	-31
17360bi1	69440i1	9765g1	5425h1	7595b1	33635o1

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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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