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	8410b	Isogeny class
Conductor	8410	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	375840	Modular degree for the optimal curve
Δ	1.3462631465606E+20	Discriminant
Eigenvalues	2+  2 5+ -1  0  2  3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-9563028,11364913232]	[a1,a2,a3,a4,a6]
Generators	[-1350531:110576278:729]	Generators of the group modulo torsion
j	229895296609/320000	j-invariant
L	4.0927776146642	L(r)(E,1)/r!
Ω	0.18425474808536	Real period
R	11.106301620971	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	67280p1 75690bm1 42050w1 8410k1	Quadratic twists by: -4 -3 5 29

Hecke Eigenvalues for elliptic curve 8410b1

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 8410b1

-4	-3	5	29
67280p1	75690bm1	42050w1	8410k1

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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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