Properties

Label 277200.fl
Number of curves $6$
Conductor $277200$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("277200.fl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277200.fl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277200.fl1 277200fl6 [0, 0, 0, -47700075, -126796099750] [2] 25165824  
277200.fl2 277200fl4 [0, 0, 0, -3150075, -1744249750] [2, 2] 12582912  
277200.fl3 277200fl2 [0, 0, 0, -972075, 344452250] [2, 2] 6291456  
277200.fl4 277200fl1 [0, 0, 0, -954075, 358690250] [2] 3145728 \(\Gamma_0(N)\)-optimal
277200.fl5 277200fl3 [0, 0, 0, 917925, 1521922250] [2] 12582912  
277200.fl6 277200fl5 [0, 0, 0, 6551925, -10369327750] [2] 25165824  

Rank

sage: E.rank()
 

The elliptic curves in class 277200.fl have rank \(2\).

Modular form 277200.2.a.fl

sage: E.q_eigenform(10)
 
\( q - q^{7} + q^{11} + 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.