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	2226b	Isogeny class
Conductor	2226	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	520164058176 = 26 · 310 · 72 · 532	Discriminant
Eigenvalues	2+ 3+  2 7+ -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2219,-21315]	[a1,a2,a3,a4,a6]
Generators	[-35:140:1]	Generators of the group modulo torsion
j	1209209052196153/520164058176	j-invariant
L	2.1579525918842	L(r)(E,1)/r!
Ω	0.72318804453411	Real period
R	2.9839439523291	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17808y2 71232bj2 6678o2 55650di2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2226b2

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

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Quadratic twists for elliptic curve 2226b2

-4	8	-3	5	-7	53
17808y2	71232bj2	6678o2	55650di2	15582k2	117978v2

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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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