Cremona's table of elliptic curves

5056 = 2⁶ · 79

Field	Data	Notes
Atkin-Lehner	2+ 79+	Signs for the Atkin-Lehner involutions
Class	5056a	Isogeny class
Conductor	5056	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	82837504 = 220 · 79	Discriminant
Eigenvalues	2+  1  1 -3 -4  7 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-225,1151]	[a1,a2,a3,a4,a6]
Generators	[19:64:1]	Generators of the group modulo torsion
j	4826809/316	j-invariant
L	4.2929743531974	L(r)(E,1)/r!
Ω	1.8871211426078	Real period
R	0.56872002759517	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	5056q1 158b1 45504m1 126400g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5056a1

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	-4	7	-4	6	6	-4	8	-10	-8	8	-3	-2	-1	0	4	-11	-6	+	-6	-15	1

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Quadratic twists for elliptic curve 5056a1

-4	8	-3	5
5056q1	158b1	45504m1	126400g1

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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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