Cremona's table of elliptic curves

4067 = 7² · 83

Field	Data	Notes
Atkin-Lehner	7- 83-	Signs for the Atkin-Lehner involutions
Class	4067b	Isogeny class
Conductor	4067	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	156	Modular degree for the optimal curve
Δ	-4067 = -1 · 72 · 83	Discriminant
Eigenvalues	0 -1  0 7-  0 -2  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-23,-36]	[a1,a2,a3,a4,a6]
Generators	[6:2:1]	Generators of the group modulo torsion
j	-28672000/83	j-invariant
L	2.3184550349452	L(r)(E,1)/r!
Ω	1.0859255926582	Real period
R	2.1350035864519	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	65072p1 36603h1 101675e1 4067a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4067b1

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	-1	0	-	0	-2	3	-2	3	6	1	5	-3	2	12	-12	-12	10	-10	-6	-2	8	-	6	16

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Quadratic twists for elliptic curve 4067b1

-4	-3	5	-7
65072p1	36603h1	101675e1	4067a1

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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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