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	8	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-57337308 = -1 · 22 · 36 · 7 · 532	Discriminant
Eigenvalues	2- 3+ -2 7-  0 -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,71,-253]	[a1,a2,a3,a4,a6]
Generators	[35:198:1]	Generators of the group modulo torsion
j	39547260143/57337308	j-invariant
L	3.5706792323684	L(r)(E,1)/r!
Ω	1.05111812754	Real period
R	1.6985147238994	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	17808r1 71232bs1 6678g1 55650w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2226i1

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 2226i1

-4	8	-3	5	-7	53
17808r1	71232bs1	6678g1	55650w1	15582u1	117978j1

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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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