Properties

Label 12144.bh
Number of curves 2
Conductor 12144
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("12144.bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12144.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12144.bh1 12144bb2 [0, 1, 0, -19808, 1058100] [2] 20480  
12144.bh2 12144bb1 [0, 1, 0, -368, 39444] [2] 10240 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 12144.bh have rank \(1\).

Modular form 12144.2.a.bh

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{7} + q^{9} - q^{11} + 2q^{13} - 2q^{19} + O(q^{20}) \)

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.