Cremona's table of elliptic curves

9086 = 2 · 7 · 11 · 59

Field	Data	Notes
Atkin-Lehner	2+ 7+ 11+ 59+	Signs for the Atkin-Lehner involutions
Class	9086a	Isogeny class
Conductor	9086	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4464	Modular degree for the optimal curve
Δ	-1391648104 = -1 · 23 · 7 · 112 · 593	Discriminant
Eigenvalues	2+  0 -1 7+ 11+ -4 -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-770,-8228]	[a1,a2,a3,a4,a6]
Generators	[33:22:1]	Generators of the group modulo torsion
j	-50525789641209/1391648104	j-invariant
L	2.4338032602694	L(r)(E,1)/r!
Ω	0.45239200691828	Real period
R	2.6899273451454	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	72688h1 81774bz1 63602f1 99946k1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 9086a1

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	-1	+	+	-4	-4	6	7	10	-2	1	4	-2	-4	0	+	4	12	-14	10	0	9	9	1

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Quadratic twists for elliptic curve 9086a1

-4	-3	-7	-11
72688h1	81774bz1	63602f1	99946k1

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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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