Properties

Label 4033.b
Number of curves $1$
Conductor $4033$
CM no
Rank $0$

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

Elliptic curves in class 4033.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4033.b1 4033b1 \([1, -1, 0, 10717, 157106]\) \(136119582814177143/89802435289753\) \(-89802435289753\) \([]\) \(7560\) \(1.3662\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4033.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 4033.b do not have complex multiplication.

Modular form 4033.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - 3 q^{8} - 3 q^{9} - 2 q^{10} + q^{11} - 5 q^{13} + 2 q^{14} - q^{16} - 3 q^{17} - 3 q^{18} + O(q^{20})\) Copy content Toggle raw display