Cremona's table of elliptic curves

2065 = 5 · 7 · 59

Field	Data	Notes
Atkin-Lehner	5- 7+ 59-	Signs for the Atkin-Lehner involutions
Class	2065b	Isogeny class
Conductor	2065	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-2065 = -1 · 5 · 7 · 59	Discriminant
Eigenvalues	-1  2 5- 7+ -3  4 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,0,2]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	-1/2065	j-invariant
L	2.738192594192	L(r)(E,1)/r!
Ω	3.697057367032	Real period
R	0.74064108893994	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	33040i1 18585e1 10325d1 14455d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2065b1

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	-	+	-3	4	-3	-5	-6	-9	8	-1	10	-6	-8	8	-	-9	-8	-6	6	4	-5	-7	-8

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Quadratic twists for elliptic curve 2065b1

-4	-3	5	-7	-59
33040i1	18585e1	10325d1	14455d1	121835g1

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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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