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	6972d	Isogeny class
Conductor	6972	Conductor
∏ cp	15	Product of Tamagawa factors cp
deg	3600	Modular degree for the optimal curve
Δ	-602631792 = -1 · 24 · 33 · 75 · 83	Discriminant
Eigenvalues	2- 3-  2 7-  2 -7  3 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-82,-1243]	[a1,a2,a3,a4,a6]
Generators	[29:147:1]	Generators of the group modulo torsion
j	-3857721088/37664487	j-invariant
L	5.5903766963489	L(r)(E,1)/r!
Ω	0.69054668308236	Real period
R	0.53970540860906	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	27888p1 111552t1 20916i1 48804h1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6972d1

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
-	-	2	-	2	-7	3	-8	0	-4	-2	-9	-5	-10	-12	3	3	-14	4	16	-1	-10	-	16	-2

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Quadratic twists for elliptic curve 6972d1

-4	8	-3	-7
27888p1	111552t1	20916i1	48804h1

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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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