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	6972a	Isogeny class
Conductor	6972	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-5270832 = -1 · 24 · 34 · 72 · 83	Discriminant
Eigenvalues	2- 3-  0 7+  4 -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,7,-108]	[a1,a2,a3,a4,a6]
Generators	[16:66:1]	Generators of the group modulo torsion
j	2048000/329427	j-invariant
L	4.9000672157469	L(r)(E,1)/r!
Ω	1.1417145636057	Real period
R	2.1459248099068	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	27888bb1 111552m1 20916g1 48804l1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6972a1

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

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Quadratic twists for elliptic curve 6972a1

-4	8	-3	-7
27888bb1	111552m1	20916g1	48804l1

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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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