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	1040f	Isogeny class
Conductor	1040	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	276889600 = 216 · 52 · 132	Discriminant
Eigenvalues	2-  0 5-  0  0 13-  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1387,19866]	[a1,a2,a3,a4,a6]
j	72043225281/67600	j-invariant
L	1.7280911161207	L(r)(E,1)/r!
Ω	1.7280911161207	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	130b2 4160j2 9360bl2 5200n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1040f2

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

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Quadratic twists for elliptic curve 1040f2

-4	8	-3	5	-7	-11	13
130b2	4160j2	9360bl2	5200n2	50960s2	125840cd2	13520n2

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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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