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	4	Product of Tamagawa factors cp
Δ	-8254129 = -1 · 134 · 172	Discriminant
Eigenvalues	1  2  2  2 -6 13+ 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-54,185]	[a1,a2,a3,a4,a6]
j	-17923019113/8254129	j-invariant
L	2.1761000761788	L(r)(E,1)/r!
Ω	2.1761000761788	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	3536l2 14144p2 1989c2 5525e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 221b2

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 221b2

-4	8	-3	5	-7	-11	13	17	-19	-23
3536l2	14144p2	1989c2	5525e2	10829b2	26741g2	2873c2	3757a2	79781e2	116909b2

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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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