Cremona's table of elliptic curves

5056 = 2⁶ · 79

Field	Data	Notes
Atkin-Lehner	2+ 79+	Signs for the Atkin-Lehner involutions
Class	5056b	Isogeny class
Conductor	5056	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	12906109962551296 = 222 · 795	Discriminant
Eigenvalues	2+  1 -1  3 -2  1 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1496321,-704984737]	[a1,a2,a3,a4,a6]
Generators	[-6571761:363392:9261]	Generators of the group modulo torsion
j	1413378216646643521/49232902384	j-invariant
L	4.4057186686499	L(r)(E,1)/r!
Ω	0.13650364409224	Real period
R	8.0688663990405	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5056r2 158c2 45504k2 126400h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5056b2

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
+	1	-1	3	-2	1	-2	0	-6	10	2	2	2	-4	3	-4	-5	-12	-8	-13	-6	+	6	-15	13

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Quadratic twists for elliptic curve 5056b2

-4	8	-3	5
5056r2	158c2	45504k2	126400h2

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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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