Properties

Label 176400.pc
Number of curves $2$
Conductor $176400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("176400.pc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176400.pc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.pc1 176400gc1 [0, 0, 0, -2649675, 634464250] [2] 6193152 \(\Gamma_0(N)\)-optimal
176400.pc2 176400gc2 [0, 0, 0, 9698325, 4869828250] [2] 12386304  

Rank

sage: E.rank()
 

The elliptic curves in class 176400.pc have rank \(0\).

Modular form 176400.2.a.pc

sage: E.q_eigenform(10)
 
\( q + 2q^{11} + 2q^{13} + 4q^{17} + O(q^{20}) \)

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.