Cremona's table of elliptic curves

2256 = 2⁴ · 3 · 47

Field	Data	Notes
Atkin-Lehner	2- 3- 47+	Signs for the Atkin-Lehner involutions
Class	2256m	Isogeny class
Conductor	2256	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	2923776 = 28 · 35 · 47	Discriminant
Eigenvalues	2- 3- -1  1 -3 -2 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-221,1191]	[a1,a2,a3,a4,a6]
Generators	[7:6:1]	Generators of the group modulo torsion
j	4684079104/11421	j-invariant
L	3.4615139250459	L(r)(E,1)/r!
Ω	2.5460393077209	Real period
R	0.1359568139639	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	564a1 9024bb1 6768s1 56400bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2256m1

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
-	-	-1	1	-3	-2	-6	6	-5	-5	10	-3	-6	-10	+	12	-8	-10	2	10	-2	-3	0	6	17

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Quadratic twists for elliptic curve 2256m1

-4	8	-3	5	-7	-47
564a1	9024bb1	6768s1	56400bs1	110544ck1	106032bf1

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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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