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	4056d	Isogeny class
Conductor	4056	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1449327279299298048 = -1 · 28 · 35 · 1312	Discriminant
Eigenvalues	2+ 3+ -4  0  2 13+  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,95260,56773716]	[a1,a2,a3,a4,a6]
Generators	[226:9476:1]	Generators of the group modulo torsion
j	77366117936/1172914587	j-invariant
L	2.3326806541239	L(r)(E,1)/r!
Ω	0.1999215557285	Real period
R	5.8339898507286	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	8112q2 32448bp2 12168t2 101400cw2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056d2

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
+	+	-4	0	2	+	2	-8	4	-6	4	-6	12	4	6	-2	14	10	4	-2	2	-8	-14	0	10

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Quadratic twists for elliptic curve 4056d2

-4	8	-3	5	13
8112q2	32448bp2	12168t2	101400cw2	312e2

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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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