Properties

Label 432.b
Number of curves $3$
Conductor $432$
CM no
Rank $1$
Graph

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

Elliptic curves in class 432.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
432.b1 432f3 \([0, 0, 0, -459, 3834]\) \(-132651/2\) \(-161243136\) \([]\) \(144\) \(0.37794\)  
432.b2 432f2 \([0, 0, 0, -219, -1654]\) \(-1167051/512\) \(-509607936\) \([]\) \(144\) \(0.37794\)  
432.b3 432f1 \([0, 0, 0, 21, 26]\) \(9261/8\) \(-884736\) \([]\) \(48\) \(-0.17136\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 432.b have rank \(1\).

Complex multiplication

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

Modular form 432.2.a.b

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