Cremona's table of elliptic curves

1040 = 2⁴ · 5 · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	1040a	Isogeny class
Conductor	1040	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	16640 = 28 · 5 · 13	Discriminant
Eigenvalues	2+  0 5+  0  4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-23,-42]	[a1,a2,a3,a4,a6]
Generators	[6:6:1]	Generators of the group modulo torsion
j	5256144/65	j-invariant
L	2.3676351838733	L(r)(E,1)/r!
Ω	2.1816867292797	Real period
R	2.1704630202842	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	520a1 4160o1 9360r1 5200e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1040a1

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	+	0	4	+	-6	-4	0	-2	4	-6	-6	-8	0	2	-4	-10	-12	4	14	16	-12	2	-2

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Quadratic twists for elliptic curve 1040a1

-4	8	-3	5	-7	-11	13
520a1	4160o1	9360r1	5200e1	50960j1	125840i1	13520h1

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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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