Properties

Label 176400.id
Number of curves 4
Conductor 176400
CM no
Rank 2
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("176400.id1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176400.id

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.id1 176400fd3 [0, 0, 0, -19848675, 34034089250] [2] 9437184  
176400.id2 176400fd2 [0, 0, 0, -1326675, 453703250] [2, 2] 4718592  
176400.id3 176400fd1 [0, 0, 0, -444675, -108130750] [2] 2359296 \(\Gamma_0(N)\)-optimal
176400.id4 176400fd4 [0, 0, 0, 3083325, 2830693250] [2] 9437184  

Rank

sage: E.rank()
 

The elliptic curves in class 176400.id have rank \(2\).

Modular form 176400.2.a.id

sage: E.q_eigenform(10)
 
\( q - 6q^{13} - 2q^{17} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.