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	8	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-3673232240108823 = -1 · 312 · 73 · 674	Discriminant
Eigenvalues	1 3- -2 7+  4  2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,33417,1716336]	[a1,a2,a3,a4,a6]
Generators	[38342:2636977:8]	Generators of the group modulo torsion
j	5660975162375567/5038727352687	j-invariant
L	3.8851681768327	L(r)(E,1)/r!
Ω	0.2887607914689	Real period
R	6.7273125223637	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	67536bw1 1407c1 105525x1 29547y1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4221d1

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 4221d1

-4	-3	5	-7
67536bw1	1407c1	105525x1	29547y1

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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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