Cremona's table of elliptic curves

221 = 13 · 17

Field	Data	Notes
Atkin-Lehner	13+ 17-	Signs for the Atkin-Lehner involutions
Class	221b	Isogeny class
Conductor	221	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	2873 = 132 · 17	Discriminant
Eigenvalues	1  2  2  2 -6 13+ 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-59,152]	[a1,a2,a3,a4,a6]
j	23320116793/2873	j-invariant
L	2.1761000761788	L(r)(E,1)/r!
Ω	4.3522001523576	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	3536l1 14144p1 1989c1 5525e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 221b1

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	2	2	2	-6	+	-	4	6	-6	-2	2	-6	0	-4	14	4	2	0	-10	10	14	12	-18	2

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Quadratic twists for elliptic curve 221b1

-4	8	-3	5	-7	-11	13	17	-19	-23
3536l1	14144p1	1989c1	5525e1	10829b1	26741g1	2873c1	3757a1	79781e1	116909b1

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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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