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	4056r	Isogeny class
Conductor	4056	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	20247552 = 210 · 32 · 133	Discriminant
Eigenvalues	2- 3- -2  2  4 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-264,-1728]	[a1,a2,a3,a4,a6]
j	907924/9	j-invariant
L	2.369471590263	L(r)(E,1)/r!
Ω	1.1847357951315	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	8112g2 32448o2 12168j2 101400p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056r2

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

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Quadratic twists for elliptic curve 4056r2

-4	8	-3	5	13
8112g2	32448o2	12168j2	101400p2	4056i2

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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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