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	4	Product of Tamagawa factors cp
Δ	-292464640 = -1 · 211 · 5 · 134	Discriminant
Eigenvalues	2+  0 5+  0  4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,157,322]	[a1,a2,a3,a4,a6]
Generators	[7:42:1]	Generators of the group modulo torsion
j	208974222/142805	j-invariant
L	2.3676351838733	L(r)(E,1)/r!
Ω	1.0908433646399	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	520a4 4160o4 9360r4 5200e4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1040a4

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 1040a4

-4	8	-3	5	-7	-11	13
520a4	4160o4	9360r4	5200e4	50960j3	125840i3	13520h4

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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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