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	8256w	Isogeny class
Conductor	8256	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	279189651456 = 224 · 32 · 432	Discriminant
Eigenvalues	2+ 3-  2  4 -4 -6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-22017,-1264545]	[a1,a2,a3,a4,a6]
Generators	[42145986757:114300595200:241804367]	Generators of the group modulo torsion
j	4502751117697/1065024	j-invariant
L	6.0012175053367	L(r)(E,1)/r!
Ω	0.39193544369025	Real period
R	15.311749937266	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8256bf2 258d2 24768bf2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 8256w2

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	-4	-6	-6	4	-4	-6	-8	-2	2	-	4	6	12	-10	-12	-8	-6	-16	12	10	2

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Quadratic twists for elliptic curve 8256w2

-4	8	-3
8256bf2	258d2	24768bf2

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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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