Cremona's table of elliptic curves

21440 = 2⁶ · 5 · 67

Field	Data	Notes
Atkin-Lehner	2+ 5+ 67+	Signs for the Atkin-Lehner involutions
Class	21440a	Isogeny class
Conductor	21440	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-22120449753088000 = -1 · 217 · 53 · 675	Discriminant
Eigenvalues	2+  0 5+  1  1  2  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-264908,52965232]	[a1,a2,a3,a4,a6]
Generators	[-291:10267:1]	Generators of the group modulo torsion
j	-15685523123710482/168765638375	j-invariant
L	5.0071351047669	L(r)(E,1)/r!
Ω	0.38316448255001	Real period
R	6.5339238535938	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	21440s1 2680a1 107200j1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 21440a1

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	+	1	1	2	2	6	4	-8	-8	9	-6	-2	-6	4	-6	7	+	-15	4	-10	-9	9	1

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Quadratic twists for elliptic curve 21440a1

-4	8	5
21440s1	2680a1	107200j1

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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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