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	4	Product of Tamagawa factors cp
deg	45472	Modular degree for the optimal curve
Δ	1160571678069520 = 24 · 5 · 299	Discriminant
Eigenvalues	2+  0 5-  4 -2  2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-35059,1931685]	[a1,a2,a3,a4,a6]
Generators	[21770:119357:125]	Generators of the group modulo torsion
j	328509/80	j-invariant
L	3.5936480334446	L(r)(E,1)/r!
Ω	0.4578746969603	Real period
R	7.848540348051	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	67280y1 75690bl1 42050ba1 8410m1	Quadratic twists by: -4 -3 5 29

Hecke Eigenvalues for elliptic curve 8410f1

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 8410f1

-4	-3	5	29
67280y1	75690bl1	42050ba1	8410m1

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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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