Properties

Label 277200kh
Number of curves 4
Conductor 277200
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("277200.kh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277200kh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277200.kh3 277200kh1 [0, 0, 0, -201675, 678384250] [2] 7962624 \(\Gamma_0(N)\)-optimal
277200.kh2 277200kh2 [0, 0, 0, -12873675, 17620848250] [2] 15925248  
277200.kh4 277200kh3 [0, 0, 0, 1814325, -18274031750] [2] 23887872  
277200.kh1 277200kh4 [0, 0, 0, -94017675, -340940375750] [2] 47775744  

Rank

sage: E.rank()
 

The elliptic curves in class 277200kh have rank \(0\).

Modular form 277200.2.a.kh

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.