Properties

Label 61200.do
Number of curves 6
Conductor 61200
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("61200.do1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 61200.do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61200.do1 61200fh6 [0, 0, 0, -99878475, -384198767750] [2] 3145728  
61200.do2 61200fh4 [0, 0, 0, -6242475, -6002963750] [2, 2] 1572864  
61200.do3 61200fh5 [0, 0, 0, -5918475, -6653879750] [2] 3145728  
61200.do4 61200fh2 [0, 0, 0, -410475, -83483750] [2, 2] 786432  
61200.do5 61200fh1 [0, 0, 0, -122475, 15300250] [2] 393216 \(\Gamma_0(N)\)-optimal
61200.do6 61200fh3 [0, 0, 0, 813525, -486179750] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 61200.do have rank \(0\).

Modular form 61200.2.a.do

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.