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	2256i	Isogeny class
Conductor	2256	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	577536 = 212 · 3 · 47	Discriminant
Eigenvalues	2- 3+ -1  3 -1 -2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-421,3469]	[a1,a2,a3,a4,a6]
Generators	[12:1:1]	Generators of the group modulo torsion
j	2019487744/141	j-invariant
L	2.7101071282446	L(r)(E,1)/r!
Ω	2.7634463918894	Real period
R	0.98069828175377	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	141e1 9024bs1 6768m1 56400ct1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2256i1

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	3	-1	-2	2	-6	-3	3	-2	-7	10	10	-	4	-8	-10	-10	14	-10	-17	-8	6	1

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Quadratic twists for elliptic curve 2256i1

-4	8	-3	5	-7	-47
141e1	9024bs1	6768m1	56400ct1	110544dm1	106032r1

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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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