Properties

Label 371280.fk
Number of curves 4
Conductor 371280
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("371280.fk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 371280.fk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
371280.fk1 371280fk3 [0, 1, 0, -11840200, 15677517428] [2] 11796480  
371280.fk2 371280fk4 [0, 1, 0, -1441480, -287893900] [2] 11796480  
371280.fk3 371280fk2 [0, 1, 0, -742600, 242975348] [2, 2] 5898240  
371280.fk4 371280fk1 [0, 1, 0, -5320, 10289780] [2] 2949120 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 371280.fk have rank \(0\).

Modular form 371280.2.a.fk

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - q^{7} + q^{9} - q^{13} + q^{15} - q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.