Cremona's table of elliptic curves

56800 = 2⁵ · 5² · 71

Field	Data	Notes
Atkin-Lehner	2+ 5+ 71+	Signs for the Atkin-Lehner involutions
Class	56800a	Isogeny class
Conductor	56800	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	267264	Modular degree for the optimal curve
Δ	71582200000000 = 29 · 58 · 713	Discriminant
Eigenvalues	2+  1 5+ -5 -2  3  4  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-35408,-2543812]	[a1,a2,a3,a4,a6]
Generators	[-133067:110150:1331]	Generators of the group modulo torsion
j	613691601992/8947775	j-invariant
L	5.2688438761334	L(r)(E,1)/r!
Ω	0.3483426621865	Real period
R	7.5627312529484	Regulator
r	1	Rank of the group of rational points
S	1.0000000000052	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	56800q1 113600i1 11360h1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 56800a1

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	+	-5	-2	3	4	7	-9	-8	5	-8	-4	7	1	10	12	-10	12	+	-1	-10	-16	9	2

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Quadratic twists for elliptic curve 56800a1

-4	8	5
56800q1	113600i1	11360h1

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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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