Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2001.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2001.b1 2001b1 \([0, -1, 1, 689, 84129]\) \(36120262639616/3095193917547\) \(-3095193917547\) \([]\) \(5760\) \(1.0762\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2001.b1 has rank \(0\).

Complex multiplication

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

Modular form 2001.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{4} + 4q^{5} - 4q^{7} + q^{9} + 4q^{11} + 2q^{12} - 5q^{13} - 4q^{15} + 4q^{16} - 5q^{17} + 5q^{19} + O(q^{20})\)  Toggle raw display