Properties

Label 73283j
Number of curves $2$
Conductor $73283$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 73283j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73283.a2 73283j1 \([1, 0, 0, -3437, -81872]\) \(-95443993/5887\) \(-276959101447\) \([2]\) \(85536\) \(0.95001\) \(\Gamma_0(N)\)-optimal
73283.a1 73283j2 \([1, 0, 0, -55782, -5075585]\) \(408023180713/1421\) \(66852196901\) \([2]\) \(171072\) \(1.2966\)  

Rank

sage: E.rank()
 

The elliptic curves in class 73283j have rank \(0\).

Complex multiplication

The elliptic curves in class 73283j do not have complex multiplication.

Modular form 73283.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 3 q^{8} + q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} - q^{14} - 4 q^{15} - q^{16} + 4 q^{17} - q^{18} + O(q^{20})\) 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 Cremona 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 Cremona labels.