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	8	Product of Tamagawa factors cp
Δ	16640000 = 211 · 54 · 13	Discriminant
Eigenvalues	2+  0 5+  0  4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-563,5138]	[a1,a2,a3,a4,a6]
Generators	[-11:100:1]	Generators of the group modulo torsion
j	9636491538/8125	j-invariant
L	2.3676351838733	L(r)(E,1)/r!
Ω	2.1816867292797	Real period
R	0.54261575507106	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	520a3 4160o3 9360r3 5200e3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1040a3

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 1040a3

-4	8	-3	5	-7	-11	13
520a3	4160o3	9360r3	5200e3	50960j4	125840i4	13520h3

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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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