Properties

Label 2001.a
Number of curves $1$
Conductor $2001$
CM no
Rank $0$

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2001.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2001.a1 2001a1 [1, 1, 1, 11, -52] [] 280 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2001.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 2001.a do not have complex multiplication.

Modular form 2001.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + 3q^{5} + q^{6} + 3q^{8} + q^{9} - 3q^{10} + 3q^{11} + q^{12} + 3q^{13} - 3q^{15} - q^{16} - q^{18} + 8q^{19} + O(q^{20})\)  Toggle raw display