Cremona's table of elliptic curves

4056 = 2³ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	4056p	Isogeny class
Conductor	4056	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-39155074608 = -1 · 24 · 3 · 138	Discriminant
Eigenvalues	2- 3-  0  0 -6 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-563,-11010]	[a1,a2,a3,a4,a6]
Generators	[111:1143:1]	Generators of the group modulo torsion
j	-256000/507	j-invariant
L	4.1460472336767	L(r)(E,1)/r!
Ω	0.46056598122453	Real period
R	4.5010350337354	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	8112a1 32448a1 12168b1 101400c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056p1

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	-6	+	2	0	4	-6	4	2	0	4	-10	-10	6	-6	12	-2	-6	-16	-6	-4	-14

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Quadratic twists for elliptic curve 4056p1

-4	8	-3	5	13
8112a1	32448a1	12168b1	101400c1	312a1

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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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