Properties

Label 277200.jq
Number of curves $6$
Conductor $277200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("jq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277200.jq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277200.jq1 277200jq6 [0, 0, 0, -10977120075, -442670657687750] [2] 94371840  
277200.jq2 277200jq4 [0, 0, 0, -686070075, -6916727537750] [2, 2] 47185920  
277200.jq3 277200jq5 [0, 0, 0, -682668075, -6988717259750] [2] 94371840  
277200.jq4 277200jq3 [0, 0, 0, -91602075, 177951690250] [2] 47185920  
277200.jq5 277200jq2 [0, 0, 0, -43092075, -106947539750] [2, 2] 23592960  
277200.jq6 277200jq1 [0, 0, 0, 125925, -4996277750] [2] 11796480 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 277200.jq do not have complex multiplication.

Modular form 277200.2.a.jq

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.