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	4221g	Isogeny class
Conductor	4221	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	15702487227 = 314 · 72 · 67	Discriminant
Eigenvalues	-1 3-  0 7-  4 -4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3110,67250]	[a1,a2,a3,a4,a6]
Generators	[-30:379:1]	Generators of the group modulo torsion
j	4561907001625/21539763	j-invariant
L	2.4727421995709	L(r)(E,1)/r!
Ω	1.2478093908153	Real period
R	0.990833302655	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	67536bq2 1407e2 105525o2 29547n2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4221g2

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

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Quadratic twists for elliptic curve 4221g2

-4	-3	5	-7
67536bq2	1407e2	105525o2	29547n2

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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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