Properties

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

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

Elliptic curves in class 432.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
432.g1 432e3 \([0, 0, 0, -1971, 44658]\) \(-1167051/512\) \(-371504185344\) \([]\) \(432\) \(0.92725\)  
432.g2 432e1 \([0, 0, 0, -51, -142]\) \(-132651/2\) \(-221184\) \([]\) \(48\) \(-0.17136\) \(\Gamma_0(N)\)-optimal
432.g3 432e2 \([0, 0, 0, 189, -702]\) \(9261/8\) \(-644972544\) \([]\) \(144\) \(0.37794\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 432.g do not have complex multiplication.

Modular form 432.2.a.g

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

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.