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	2226d	Isogeny class
Conductor	2226	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-1121904 = -1 · 24 · 33 · 72 · 53	Discriminant
Eigenvalues	2+ 3+  2 7- -6  2  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,21,45]	[a1,a2,a3,a4,a6]
Generators	[2:9:1]	Generators of the group modulo torsion
j	949862087/1121904	j-invariant
L	2.2491118390637	L(r)(E,1)/r!
Ω	1.8371460669014	Real period
R	1.2242422524722	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	17808u1 71232bo1 6678q1 55650cw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2226d1

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
+	+	2	-	-6	2	4	0	-8	-6	4	-6	2	-8	-8	-	8	0	2	-8	4	-10	12	-16	10

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Quadratic twists for elliptic curve 2226d1

-4	8	-3	5	-7	53
17808u1	71232bo1	6678q1	55650cw1	15582n1	117978y1

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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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