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	2226h	Isogeny class
Conductor	2226	Conductor
∏ cp	156	Product of Tamagawa factors cp
deg	4992	Modular degree for the optimal curve
Δ	-4840593924096 = -1 · 213 · 34 · 72 · 533	Discriminant
Eigenvalues	2- 3+  1 7+ -1  0 -7 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,2710,-89737]	[a1,a2,a3,a4,a6]
Generators	[561:13075:1]	Generators of the group modulo torsion
j	2201007734483039/4840593924096	j-invariant
L	3.9295523507095	L(r)(E,1)/r!
Ω	0.39972397881638	Real period
R	0.063017080486795	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	17808bd1 71232y1 6678c1 55650bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2226h1

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	0	-7	-4	-7	-8	9	-4	6	5	12	-	-5	-6	-8	-4	-2	-15	-4	-9	1

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Quadratic twists for elliptic curve 2226h1

-4	8	-3	5	-7	53
17808bd1	71232y1	6678c1	55650bb1	15582y1	117978d1

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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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