Properties

Label 273600.oj
Number of curves $4$
Conductor $273600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("oj1")
 
E.isogeny_class()
 

Elliptic curves in class 273600.oj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273600.oj1 273600oj3 \([0, 0, 0, -13932300, 20012182000]\) \(100162392144121/23457780\) \(70044555755520000000\) \([2]\) \(18874368\) \(2.7984\)  
273600.oj2 273600oj4 \([0, 0, 0, -6444300, -6123242000]\) \(9912050027641/311647500\) \(930574448640000000000\) \([2]\) \(18874368\) \(2.7984\)  
273600.oj3 273600oj2 \([0, 0, 0, -972300, 235222000]\) \(34043726521/11696400\) \(34925263257600000000\) \([2, 2]\) \(9437184\) \(2.4519\)  
273600.oj4 273600oj1 \([0, 0, 0, 179700, 25558000]\) \(214921799/218880\) \(-653572177920000000\) \([2]\) \(4718592\) \(2.1053\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 273600.oj have rank \(1\).

Complex multiplication

The elliptic curves in class 273600.oj do not have complex multiplication.

Modular form 273600.2.a.oj

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