Properties

Label 369600.oc
Number of curves $4$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("oc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.oc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.oc1 369600oc4 \([0, 1, 0, -8132033, -8928503937]\) \(116158555210501448/4764375\) \(2439360000000000\) \([2]\) \(9437184\) \(2.4394\)  
369600.oc2 369600oc3 \([0, 1, 0, -824033, 53280063]\) \(120861530858888/67523047515\) \(34571800327680000000\) \([2]\) \(9437184\) \(2.4394\)  
369600.oc3 369600oc2 \([0, 1, 0, -509033, -139184937]\) \(227919983840704/1452753225\) \(92976206400000000\) \([2, 2]\) \(4718592\) \(2.0928\)  
369600.oc4 369600oc1 \([0, 1, 0, -12908, -4735062]\) \(-237867017536/9530541405\) \(-9530541405000000\) \([2]\) \(2359296\) \(1.7462\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 369600.oc have rank \(0\).

Complex multiplication

The elliptic curves in class 369600.oc do not have complex multiplication.

Modular form 369600.2.a.oc

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} - q^{11} + 6 q^{13} - 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

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.