Cremona's table of elliptic curves

9256 = 2³ · 13 · 89

Field	Data	Notes
Atkin-Lehner	2- 13+ 89+	Signs for the Atkin-Lehner involutions
Class	9256c	Isogeny class
Conductor	9256	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	11232	Modular degree for the optimal curve
Δ	296192 = 28 · 13 · 89	Discriminant
Eigenvalues	2- -2 -4  3 -2 13+  7  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6945,-225101]	[a1,a2,a3,a4,a6]
j	144731488592896/1157	j-invariant
L	1.0459388077461	L(r)(E,1)/r!
Ω	0.52296940387303	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18512b1 74048i1 83304j1 120328c1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 9256c1

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	-4	3	-2	+	7	3	8	6	4	2	5	-10	-8	-9	-1	10	4	6	-14	-9	1	+	12

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Quadratic twists for elliptic curve 9256c1

-4	8	-3	13
18512b1	74048i1	83304j1	120328c1

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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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