Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
72450.m2 72450bf1 [1, -1, 0, -43317, 3411841] [2] 368640 \(\Gamma_0(N)\)-optimal
72450.m1 72450bf2 [1, -1, 0, -95067, -6265409] [2] 737280  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 72450.2.a.bf

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.