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	6	Product of Tamagawa factors cp
Δ	1381408203125000 = 23 · 512 · 294	Discriminant
Eigenvalues	2- -2 5+ -1  0  2 -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-45011,-3215015]	[a1,a2,a3,a4,a6]
Generators	[-3804:17527:27]	Generators of the group modulo torsion
j	14258975033569/1953125000	j-invariant
L	3.9977156902335	L(r)(E,1)/r!
Ω	0.3307473949789	Real period
R	2.0144858538183	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	67280u2 75690u2 42050n2 8410b2	Quadratic twists by: -4 -3 5 29

Hecke Eigenvalues for elliptic curve 8410k2

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 8410k2

-4	-3	5	29
67280u2	75690u2	42050n2	8410b2

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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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