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	2067a	Isogeny class
Conductor	2067	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	-1506843 = -1 · 37 · 13 · 53	Discriminant
Eigenvalues	-2 3- -2  2 -3 13+  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-164,758]	[a1,a2,a3,a4,a6]
Generators	[4:13:1]	Generators of the group modulo torsion
j	-490795651072/1506843	j-invariant
L	1.7622657360735	L(r)(E,1)/r!
Ω	2.6938717513845	Real period
R	0.093453687199889	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	33072m1 6201c1 51675i1 101283n1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2067a1

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
-2	-	-2	2	-3	+	0	7	-5	0	-4	4	-8	-1	0	-	3	4	-1	6	2	-10	-12	-2	8

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Quadratic twists for elliptic curve 2067a1

-4	-3	5	-7	13	53
33072m1	6201c1	51675i1	101283n1	26871f1	109551c1

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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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