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	8410f	Isogeny class
Conductor	8410	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1450714597586900 = 22 · 52 · 299	Discriminant
Eigenvalues	2+  0 5-  4 -2  2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-522839,145631673]	[a1,a2,a3,a4,a6]
Generators	[452:999:1]	Generators of the group modulo torsion
j	1089547389/100	j-invariant
L	3.5936480334446	L(r)(E,1)/r!
Ω	0.4578746969603	Real period
R	3.9242701740255	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	67280y2 75690bl2 42050ba2 8410m2	Quadratic twists by: -4 -3 5 29

Hecke Eigenvalues for elliptic curve 8410f2

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	-2	2	-6	-2	0	-	10	-6	-12	-4	8	-2	-12	4	8	8	-2	10	-4	12	2

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Quadratic twists for elliptic curve 8410f2

-4	-3	5	29
67280y2	75690bl2	42050ba2	8410m2

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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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