Properties

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

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

Elliptic curves in class 176400.pc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.pc1 176400gc1 \([0, 0, 0, -2649675, 634464250]\) \(1092727/540\) \(1016678459623680000000\) \([2]\) \(6193152\) \(2.7240\) \(\Gamma_0(N)\)-optimal
176400.pc2 176400gc2 \([0, 0, 0, 9698325, 4869828250]\) \(53582633/36450\) \(-68625796024598400000000\) \([2]\) \(12386304\) \(3.0706\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 176400.pc do not have complex multiplication.

Modular form 176400.2.a.pc

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.