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	1056b	Isogeny class
Conductor	1056	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	13381632 = 212 · 33 · 112	Discriminant
Eigenvalues	2+ 3+ -2  2 11+ -2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-129,-495]	[a1,a2,a3,a4,a6]
Generators	[-7:4:1]	Generators of the group modulo torsion
j	58411072/3267	j-invariant
L	2.0757730771315	L(r)(E,1)/r!
Ω	1.4206395637021	Real period
R	0.73057696342139	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	1056f2 2112bb1 3168y2 26400bw2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1056b2

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

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Quadratic twists for elliptic curve 1056b2

-4	8	-3	5	-7	-11
1056f2	2112bb1	3168y2	26400bw2	51744bm2	11616u2

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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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