Cremona's table of elliptic curves

8526 = 2 · 3 · 7² · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 29+	Signs for the Atkin-Lehner involutions
Class	8526m	Isogeny class
Conductor	8526	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	864117595082478492 = 22 · 32 · 79 · 296	Discriminant
Eigenvalues	2- 3+  0 7-  0 -2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-283858,37139843]	[a1,a2,a3,a4,a6]
Generators	[-71:7581:1]	Generators of the group modulo torsion
j	21500025903924625/7344878367708	j-invariant
L	5.4768704439566	L(r)(E,1)/r!
Ω	0.25854133704189	Real period
R	2.647966523758	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	68208cf4 25578u4 1218k4	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 8526m4

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	-	0	-2	6	-8	6	+	-8	2	6	-10	0	6	0	4	-4	-6	-8	-10	0	-6	-8

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Quadratic twists for elliptic curve 8526m4

-4	-3	-7
68208cf4	25578u4	1218k4

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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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