Cremona's table of elliptic curves

8410 = 2 · 5 · 29²

Field	Data	Notes
Atkin-Lehner	2- 5+ 29-	Signs for the Atkin-Lehner involutions
Class	8410k	Isogeny class
Conductor	8410	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	12960	Modular degree for the optimal curve
Δ	226329920000 = 29 · 54 · 294	Discriminant
Eigenvalues	2- -2 5+ -1  0  2 -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-11371,465201]	[a1,a2,a3,a4,a6]
Generators	[-104:777:1]	Generators of the group modulo torsion
j	229895296609/320000	j-invariant
L	3.9977156902335	L(r)(E,1)/r!
Ω	0.9922421849367	Real period
R	0.6714952846061	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	67280u1 75690u1 42050n1 8410b1	Quadratic twists by: -4 -3 5 29

Hecke Eigenvalues for elliptic curve 8410k1

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
-	-2	+	-1	0	2	-3	2	-3	-	5	2	-6	-10	3	6	0	8	2	3	11	11	-12	3	-7

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Quadratic twists for elliptic curve 8410k1

-4	-3	5	29
67280u1	75690u1	42050n1	8410b1

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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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