Cremona's table of elliptic curves

8260 = 2² · 5 · 7 · 59

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 59-	Signs for the Atkin-Lehner involutions
Class	8260c	Isogeny class
Conductor	8260	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-1156400 = -1 · 24 · 52 · 72 · 59	Discriminant
Eigenvalues	2-  0 5- 7-  2 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,8,-51]	[a1,a2,a3,a4,a6]
Generators	[114:435:8]	Generators of the group modulo torsion
j	3538944/72275	j-invariant
L	4.5270145685459	L(r)(E,1)/r!
Ω	1.3330994274268	Real period
R	3.3958566596073	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	33040f1 74340o1 41300a1 57820d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8260c1

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	-	-	2	-2	-2	-4	8	6	-4	-8	-6	-12	6	6	-	8	-8	0	-2	-16	-6	8	18

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Quadratic twists for elliptic curve 8260c1

-4	-3	5	-7
33040f1	74340o1	41300a1	57820d1

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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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