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	2226a	Isogeny class
Conductor	2226	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-586381824 = -1 · 29 · 32 · 74 · 53	Discriminant
Eigenvalues	2+ 3+ -1 7+ -1  2  1 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-37243,2750941]	[a1,a2,a3,a4,a6]
Generators	[115:16:1]	Generators of the group modulo torsion
j	-5713153642029363769/586381824	j-invariant
L	1.8229467033551	L(r)(E,1)/r!
Ω	1.2580023751393	Real period
R	0.36227012352682	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	17808w1 71232bc1 6678l1 55650db1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2226a1

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	+	-1	2	1	-2	3	-4	7	10	0	-5	-6	+	-3	10	10	-16	-14	-3	-6	7	-1

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Quadratic twists for elliptic curve 2226a1

-4	8	-3	5	-7	53
17808w1	71232bc1	6678l1	55650db1	15582j1	117978t1

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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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