Cremona's table of elliptic curves

2226 = 2 · 3 · 7 · 53

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 53+	Signs for the Atkin-Lehner involutions
Class	2226f	Isogeny class
Conductor	2226	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-36648864 = -1 · 25 · 32 · 74 · 53	Discriminant
Eigenvalues	2+ 3- -1 7-  3 -6 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,81,-62]	[a1,a2,a3,a4,a6]
Generators	[2:9:1]	Generators of the group modulo torsion
j	59822347031/36648864	j-invariant
L	2.6623460547973	L(r)(E,1)/r!
Ω	1.1907261749078	Real period
R	0.27948764700283	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	17808m1 71232r1 6678t1 55650bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2226f1

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	-6	-3	-2	3	-4	-5	2	-8	-5	2	+	9	-6	2	16	-6	-7	2	-13	-17

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Quadratic twists for elliptic curve 2226f1

-4	8	-3	5	-7	53
17808m1	71232r1	6678t1	55650bz1	15582d1	117978q1

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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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