Cremona's table of elliptic curves

221 = 13 · 17

Field	Data	Notes
Atkin-Lehner	13+ 17-	Signs for the Atkin-Lehner involutions
Class	221a	Isogeny class
Conductor	221	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	82055753 = 136 · 17	Discriminant
Eigenvalues	-1  0  4 -2  6 13+ 17-  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-733,7804]	[a1,a2,a3,a4,a6]
j	43499078731809/82055753	j-invariant
L	0.96251248411225	L(r)(E,1)/r!
Ω	1.9250249682245	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3536i1 14144m1 1989b1 5525d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 221a1

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

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Quadratic twists for elliptic curve 221a1

-4	8	-3	5	-7	-11	13	17	-19	-23
3536i1	14144m1	1989b1	5525d1	10829c1	26741f1	2873b1	3757b1	79781d1	116909c1

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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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