Properties

Label 432.g
Number of curves $3$
Conductor $432$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("432.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 432.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
432.g1 432e3 [0, 0, 0, -1971, 44658] [] 432  
432.g2 432e1 [0, 0, 0, -51, -142] [] 48 \(\Gamma_0(N)\)-optimal
432.g3 432e2 [0, 0, 0, 189, -702] [] 144  

Rank

sage: E.rank()
 

The elliptic curves in class 432.g have rank \(0\).

Modular form 432.2.a.g

sage: E.q_eigenform(10)
 
\( q + 3q^{5} + q^{7} + 3q^{11} - 4q^{13} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.