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	2256a	Isogeny class
Conductor	2256	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	2923776 = 28 · 35 · 47	Discriminant
Eigenvalues	2+ 3+ -1  1  1 -4 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-81,-243]	[a1,a2,a3,a4,a6]
Generators	[-4:1:1]	Generators of the group modulo torsion
j	232428544/11421	j-invariant
L	2.6002472981177	L(r)(E,1)/r!
Ω	1.5946105150039	Real period
R	1.6306472794777	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	1128a1 9024bo1 6768d1 56400s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2256a1

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	1	-4	-4	6	3	7	-8	-3	-2	4	+	2	2	-14	8	-10	4	-15	6	-6	-11

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Quadratic twists for elliptic curve 2256a1

-4	8	-3	5	-7	-47
1128a1	9024bo1	6768d1	56400s1	110544bm1	106032b1

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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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