Properties

Label 61200fd
Number of curves 4
Conductor 61200
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("61200.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 61200fd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61200.w4 61200fd1 [0, 0, 0, -10875, 270250] [2] 165888 \(\Gamma_0(N)\)-optimal
61200.w3 61200fd2 [0, 0, 0, -154875, 23454250] [2] 331776  
61200.w2 61200fd3 [0, 0, 0, -370875, -86921750] [2] 497664  
61200.w1 61200fd4 [0, 0, 0, -406875, -69029750] [2] 995328  

Rank

sage: E.rank()
 

The elliptic curves in class 61200fd have rank \(1\).

Modular form 61200.2.a.w

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.