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	4056k	Isogeny class
Conductor	4056	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-626481193728 = -1 · 28 · 3 · 138	Discriminant
Eigenvalues	2- 3+  0  4  2 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1972,-18396]	[a1,a2,a3,a4,a6]
j	686000/507	j-invariant
L	2.0467745511211	L(r)(E,1)/r!
Ω	0.51169363778026	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	8112j2 32448w2 12168c2 101400bl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056k2

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

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Quadratic twists for elliptic curve 4056k2

-4	8	-3	5	13
8112j2	32448w2	12168c2	101400bl2	312b2

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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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