Cremona's table of elliptic curves

1056 = 2⁵ · 3 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 11+	Signs for the Atkin-Lehner involutions
Class	1056i	Isogeny class
Conductor	1056	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	36951552 = 29 · 38 · 11	Discriminant
Eigenvalues	2- 3- -2  0 11+ -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-144,-648]	[a1,a2,a3,a4,a6]
Generators	[-6:6:1]	Generators of the group modulo torsion
j	649461896/72171	j-invariant
L	2.6111870785783	L(r)(E,1)/r!
Ω	1.3873367614991	Real period
R	0.47053951698015	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	1056c3 2112f3 3168m3 26400c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1056i2

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

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Quadratic twists for elliptic curve 1056i2

-4	8	-3	5	-7	-11
1056c3	2112f3	3168m3	26400c3	51744by3	11616m3

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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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