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Properties

Label 72450c
Number of curves $2$
Conductor $72450$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
72450.i2 72450c1 [1, -1, 0, 318633, 75024541] [] 1347840 \(\Gamma_0(N)\)-optimal
72450.i1 72450c2 [1, -1, 0, -3131367, -3339325459] [] 4043520  

Rank

sage: E.rank()
 

The elliptic curves in class 72450c have rank \(1\).

Complex multiplication

The elliptic curves in class 72450c do not have complex multiplication.

Modular form 72450.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{7} - q^{8} - 3q^{11} + 4q^{13} + q^{14} + q^{16} + 6q^{17} - q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.