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	4	Product of Tamagawa factors cp
Δ	111105792 = 28 · 32 · 7 · 832	Discriminant
Eigenvalues	2- 3-  0 7+  4 -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-308,-2124]	[a1,a2,a3,a4,a6]
Generators	[170:297:8]	Generators of the group modulo torsion
j	12663250000/434007	j-invariant
L	4.9000672157469	L(r)(E,1)/r!
Ω	1.1417145636057	Real period
R	4.2918496198137	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	27888bb2 111552m2 20916g2 48804l2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6972a2

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 6972a2

-4	8	-3	-7
27888bb2	111552m2	20916g2	48804l2

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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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