Cremona's table of elliptic curves

4067 = 7² · 83

Field	Data	Notes
Atkin-Lehner	7- 83-	Signs for the Atkin-Lehner involutions
Class	4067c	Isogeny class
Conductor	4067	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	660	Modular degree for the optimal curve
Δ	-9764867 = -1 · 76 · 83	Discriminant
Eigenvalues	-1  1  2 7-  3  6 -5 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,48,83]	[a1,a2,a3,a4,a6]
Generators	[1:11:1]	Generators of the group modulo torsion
j	103823/83	j-invariant
L	3.1444062183005	L(r)(E,1)/r!
Ω	1.4794771535745	Real period
R	2.1253496282138	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	65072s1 36603n1 101675f1 83a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4067c1

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	1	2	-	3	6	-5	-2	-4	-7	-5	-11	2	-8	0	6	-5	-5	-2	2	0	14	-	0	8

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Quadratic twists for elliptic curve 4067c1

-4	-3	5	-7
65072s1	36603n1	101675f1	83a1

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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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