Cremona's table of elliptic curves

6972 = 2² · 3 · 7 · 83

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 83-	Signs for the Atkin-Lehner involutions
Class	6972c	Isogeny class
Conductor	6972	Conductor
∏ cp	168	Product of Tamagawa factors cp
Δ	7294006453606371072 = 28 · 36 · 77 · 834	Discriminant
Eigenvalues	2- 3-  0 7- -2 -2 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4330228,3464402900]	[a1,a2,a3,a4,a6]
Generators	[-1813:73206:1]	Generators of the group modulo torsion
j	35076490851064314706000/28492212709399887	j-invariant
L	4.9514562373235	L(r)(E,1)/r!
Ω	0.23358669226872	Real period
R	0.50470261824139	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	27888n2 111552q2 20916h2 48804c2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6972c2

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	-2	-4	4	6	-10	0	2	-8	0	12	-14	-8	-2	4	6	-14	0	-	-4	10

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Quadratic twists for elliptic curve 6972c2

-4	8	-3	-7
27888n2	111552q2	20916h2	48804c2

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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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