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
Δ	634933 = 133 · 172	Discriminant
Eigenvalues	-1  0  4 -2  6 13+ 17-  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-11718,491144]	[a1,a2,a3,a4,a6]
j	177930109857804849/634933	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	3536i2 14144m2 1989b2 5525d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 221a2

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 221a2

-4	8	-3	5	-7	-11	13	17	-19	-23
3536i2	14144m2	1989b2	5525d2	10829c2	26741f2	2873b2	3757b2	79781d2	116909c2

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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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