Cremona's table of elliptic curves

4221 = 3² · 7 · 67

Field	Data	Notes
Atkin-Lehner	3- 7+ 67-	Signs for the Atkin-Lehner involutions
Class	4221d	Isogeny class
Conductor	4221	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	4731584106667128669 = 330 · 73 · 67	Discriminant
Eigenvalues	1 3- -2 7+  4  2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1202733,-496489500]	[a1,a2,a3,a4,a6]
Generators	[-1807912381906241412648:-7887367366043953548291:2766783085774636544]	Generators of the group modulo torsion
j	263939304644887918033/6490513177869861	j-invariant
L	3.8851681768327	L(r)(E,1)/r!
Ω	0.14438039573445	Real period
R	26.909250089455	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	67536bw3 1407c4 105525x3 29547y3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4221d3

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	+	4	2	6	-8	0	2	8	-10	-6	4	4	2	0	-14	-	0	2	-8	-16	14	-18

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Quadratic twists for elliptic curve 4221d3

-4	-3	5	-7
67536bw3	1407c4	105525x3	29547y3

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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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