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	2256l	Isogeny class
Conductor	2256	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-140341248 = -1 · 212 · 36 · 47	Discriminant
Eigenvalues	2- 3-  0 -4  0  6 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-128,756]	[a1,a2,a3,a4,a6]
Generators	[4:18:1]	Generators of the group modulo torsion
j	-57066625/34263	j-invariant
L	3.3947432065732	L(r)(E,1)/r!
Ω	1.7035425394372	Real period
R	0.33212586203794	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	141b1 9024ba1 6768r1 56400bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2256l1

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	-4	0	6	-6	-2	-4	8	-6	-6	-8	6	+	2	-12	2	2	0	-10	4	-4	-10	-18

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Quadratic twists for elliptic curve 2256l1

-4	8	-3	5	-7	-47
141b1	9024ba1	6768r1	56400bv1	110544cf1	106032be1

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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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