Properties

Label 283920.o
Number of curves $2$
Conductor $283920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 283920.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.o1 283920o1 \([0, -1, 0, -5556776, -5039823504]\) \(959781554388721/19377540\) \(383105779588546560\) \([2]\) \(7741440\) \(2.4942\) \(\Gamma_0(N)\)-optimal
283920.o2 283920o2 \([0, -1, 0, -5367496, -5399304080]\) \(-865005601073041/136840035150\) \(-2705410921358689689600\) \([2]\) \(15482880\) \(2.8408\)  

Rank

sage: E.rank()
 

The elliptic curves in class 283920.o have rank \(0\).

Complex multiplication

The elliptic curves in class 283920.o do not have complex multiplication.

Modular form 283920.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + 2 q^{11} + q^{15} - 4 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.