Properties

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

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 72450.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.bd1 72450bw2 \([1, -1, 0, -14022, 639036]\) \(3346058125493/21595896\) \(1967926023000\) \([2]\) \(184320\) \(1.1954\)  
72450.bd2 72450bw1 \([1, -1, 0, -1422, -3564]\) \(3491055413/1947456\) \(177461928000\) \([2]\) \(92160\) \(0.84880\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 72450.2.a.bd

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