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	1040d	Isogeny class
Conductor	1040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-182790400 = -1 · 28 · 52 · 134	Discriminant
Eigenvalues	2- -2 5+ -2 -4 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-276,-1976]	[a1,a2,a3,a4,a6]
j	-9115564624/714025	j-invariant
L	0.58286020417879	L(r)(E,1)/r!
Ω	0.58286020417879	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	260a2 4160p2 9360bv2 5200z2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1040d2

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

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Quadratic twists for elliptic curve 1040d2

-4	8	-3	5	-7	-11	13
260a2	4160p2	9360bv2	5200z2	50960ce2	125840bz2	13520bd2

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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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