Properties

Label 127296h
Number of curves $6$
Conductor $127296$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("127296.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 127296h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
127296.bb4 127296h1 [0, 0, 0, -310476, -66587024] [2] 524288 \(\Gamma_0(N)\)-optimal
127296.bb3 127296h2 [0, 0, 0, -313356, -65288720] [2, 2] 1048576  
127296.bb5 127296h3 [0, 0, 0, 127284, -234318224] [2] 2097152  
127296.bb2 127296h4 [0, 0, 0, -800076, 186832240] [2, 2] 2097152  
127296.bb6 127296h5 [0, 0, 0, 2232564, 1265239024] [2] 4194304  
127296.bb1 127296h6 [0, 0, 0, -11620236, 15244166896] [2] 4194304  

Rank

sage: E.rank()
 

The elliptic curves in class 127296h have rank \(0\).

Modular form 127296.2.a.bb

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + 4q^{11} - q^{13} - q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.