Cremona's table of elliptic curves

6321 = 3 · 7² · 43

Field	Data	Notes
Atkin-Lehner	3- 7- 43-	Signs for the Atkin-Lehner involutions
Class	6321f	Isogeny class
Conductor	6321	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	7838223309 = 312 · 73 · 43	Discriminant
Eigenvalues	-1 3- -2 7- -4 -4 -8 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1499,21804]	[a1,a2,a3,a4,a6]
Generators	[-41:142:1] [1:142:1]	Generators of the group modulo torsion
j	1086056947639/22851963	j-invariant
L	3.6505465104006	L(r)(E,1)/r!
Ω	1.3147995736906	Real period
R	0.46275069643676	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	101136bh2 18963l2 6321d2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6321f2

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	-4	-8	-8	-8	-10	10	2	0	-	-2	-6	6	-2	-12	12	-6	-8	10	6	16

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Quadratic twists for elliptic curve 6321f2

-4	-3	-7
101136bh2	18963l2	6321d2

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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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