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	4056a	Isogeny class
Conductor	4056	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	88967743488 = 211 · 32 · 136	Discriminant
Eigenvalues	2+ 3+  2  0 -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-64952,-6349812]	[a1,a2,a3,a4,a6]
Generators	[7294398:1340412515:216]	Generators of the group modulo torsion
j	3065617154/9	j-invariant
L	3.4242523920366	L(r)(E,1)/r!
Ω	0.29905491320771	Real period
R	11.450246228385	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	8112k5 32448bh6 12168q5 101400cz6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056a5

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

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Quadratic twists for elliptic curve 4056a5

-4	8	-3	5	13
8112k5	32448bh6	12168q5	101400cz6	24a5

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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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