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	4221f	Isogeny class
Conductor	4221	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	-193857867 = -1 · 310 · 72 · 67	Discriminant
Eigenvalues	0 3-  2 7-  0  0 -1 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-264,-1782]	[a1,a2,a3,a4,a6]
Generators	[26:94:1]	Generators of the group modulo torsion
j	-2791309312/265923	j-invariant
L	3.5316246721781	L(r)(E,1)/r!
Ω	0.58901119599165	Real period
R	1.4989633033343	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	67536bt1 1407d1 105525n1 29547k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4221f1

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
0	-	2	-	0	0	-1	-3	-5	5	-10	-1	12	-8	-1	-6	-3	-12	+	8	11	-14	4	-1	-8

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Quadratic twists for elliptic curve 4221f1

-4	-3	5	-7
67536bt1	1407d1	105525n1	29547k1

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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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