Cremona's table of elliptic curves

2067 = 3 · 13 · 53

Field	Data	Notes
Atkin-Lehner	3- 13- 53+	Signs for the Atkin-Lehner involutions
Class	2067b	Isogeny class
Conductor	2067	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-3143907 = -1 · 33 · 133 · 53	Discriminant
Eigenvalues	0 3-  0 -4  3 13-  6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-13,-92]	[a1,a2,a3,a4,a6]
Generators	[26:133:1]	Generators of the group modulo torsion
j	-262144000/3143907	j-invariant
L	2.8487044499869	L(r)(E,1)/r!
Ω	1.0758262157009	Real period
R	2.6479225068251	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	33072o1 6201e1 51675c1 101283b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2067b1

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	-	0	-4	3	-	6	-7	3	6	-4	-10	-12	-1	0	+	-3	-10	5	-12	-10	-4	6	6	-16

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Quadratic twists for elliptic curve 2067b1

-4	-3	5	-7	13	53
33072o1	6201e1	51675c1	101283b1	26871c1	109551e1

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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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