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Properties

Label 73920l
Number of curves $2$
Conductor $73920$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 73920l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
73920.bl2 73920l1 [0, -1, 0, -35761, 3060211] [] 480000 \(\Gamma_0(N)\)-optimal
73920.bl1 73920l2 [0, -1, 0, -107161, -255232229] [] 2400000  

Rank

sage: E.rank()
 

The elliptic curves in class 73920l have rank \(0\).

Complex multiplication

The elliptic curves in class 73920l do not have complex multiplication.

Modular form 73920.2.a.l

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{7} + q^{9} - q^{11} + 6q^{13} + q^{15} - 7q^{17} + 5q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.