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	2226i	Isogeny class
Conductor	2226	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2760304554 = 2 · 312 · 72 · 53	Discriminant
Eigenvalues	2- 3+ -2 7-  0 -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-459,-3009]	[a1,a2,a3,a4,a6]
Generators	[-114:291:8]	Generators of the group modulo torsion
j	10695987909937/2760304554	j-invariant
L	3.5706792323684	L(r)(E,1)/r!
Ω	1.05111812754	Real period
R	3.3970294477989	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	17808r2 71232bs2 6678g2 55650w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2226i2

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	-	0	-4	2	0	-4	6	-2	-6	-8	4	-4	+	-14	-6	-4	-4	16	-4	-12	-2	-14

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Quadratic twists for elliptic curve 2226i2

-4	8	-3	5	-7	53
17808r2	71232bs2	6678g2	55650w2	15582u2	117978j2

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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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