Properties

Label 277200.ba
Number of curves 4
Conductor 277200
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("277200.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277200.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277200.ba1 277200ba3 [0, 0, 0, -118767675, 498184438250] [2] 28311552  
277200.ba2 277200ba2 [0, 0, 0, -7635675, 7314394250] [2, 2] 14155776  
277200.ba3 277200ba1 [0, 0, 0, -1803675, -809581750] [2] 7077888 \(\Gamma_0(N)\)-optimal
277200.ba4 277200ba4 [0, 0, 0, 10184325, 36378814250] [2] 28311552  

Rank

sage: E.rank()
 

The elliptic curves in class 277200.ba have rank \(1\).

Modular form 277200.2.a.ba

sage: E.q_eigenform(10)
 
\( q - q^{7} - q^{11} - 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 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.