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	4056o	Isogeny class
Conductor	4056	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	316368 = 24 · 32 · 133	Discriminant
Eigenvalues	2- 3+  0  2  2 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-43,-92]	[a1,a2,a3,a4,a6]
Generators	[-3:1:1]	Generators of the group modulo torsion
j	256000/9	j-invariant
L	3.3267918430767	L(r)(E,1)/r!
Ω	1.8647955195759	Real period
R	0.89199909806554	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	8112s1 32448bt1 12168i1 101400bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056o1

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	2	2	-	-2	-6	0	-2	-2	4	4	4	-10	-10	-6	-2	2	-6	-16	8	14	12	-8

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Quadratic twists for elliptic curve 4056o1

-4	8	-3	5	13
8112s1	32448bt1	12168i1	101400bp1	4056e1

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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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