Properties

Label 111573.bd
Number of curves 2
Conductor 111573
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("111573.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 111573.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
111573.bd1 111573p2 [1, -1, 0, -545967, -153929322] [2] 921600  
111573.bd2 111573p1 [1, -1, 0, -10152, -5722893] [2] 460800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 111573.bd have rank \(1\).

Modular form 111573.2.a.bd

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 3q^{8} - q^{11} - 2q^{13} - q^{16} - 2q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.