Cremona's table of elliptic curves

8256 = 2⁶ · 3 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3+ 43+	Signs for the Atkin-Lehner involutions
Class	8256a	Isogeny class
Conductor	8256	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	6340608 = 214 · 32 · 43	Discriminant
Eigenvalues	2+ 3+  0  0  2 -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-913,-10319]	[a1,a2,a3,a4,a6]
Generators	[37:72:1]	Generators of the group modulo torsion
j	5142706000/387	j-invariant
L	3.5702037809265	L(r)(E,1)/r!
Ω	0.86844873848499	Real period
R	2.0555063429274	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	8256bo2 516c2 24768i2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 8256a2

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	6	-4	2	8	0	-6	6	+	-6	6	10	-6	-4	-16	14	-8	6	8	-2

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Quadratic twists for elliptic curve 8256a2

-4	8	-3
8256bo2	516c2	24768i2

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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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