Cremona's table of elliptic curves

16810 = 2 · 5 · 41²

Field	Data	Notes
Atkin-Lehner	2+ 5- 41+	Signs for the Atkin-Lehner involutions
Class	16810c	Isogeny class
Conductor	16810	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	10240	Modular degree for the optimal curve
Δ	689210000 = 24 · 54 · 413	Discriminant
Eigenvalues	2+  0 5- -4  0 -4  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-479,-3715]	[a1,a2,a3,a4,a6]
Generators	[-14:17:1] [-11:17:1]	Generators of the group modulo torsion
j	176558481/10000	j-invariant
L	5.0085148666101	L(r)(E,1)/r!
Ω	1.0240119186027	Real period
R	1.2227677177444	Regulator
r	2	Rank of the group of rational points
S	0.99999999999972	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	84050h1 16810b1	Quadratic twists by: 5 41

Hecke Eigenvalues for elliptic curve 16810c1

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	-	-4	0	-4	0	-8	8	-4	-8	-6	+	4	-12	-4	-12	2	-8	-12	-6	12	12	0	-16

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Quadratic twists for elliptic curve 16810c1

5	41
84050h1	16810b1

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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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