Properties

Label 72450.du
Number of curves $2$
Conductor $72450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("du1")
 
E.isogeny_class()
 

Elliptic curves in class 72450.du

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.du1 72450dy1 \([1, -1, 1, -55130, -4742503]\) \(1626794704081/83462400\) \(950688900000000\) \([2]\) \(589824\) \(1.6319\) \(\Gamma_0(N)\)-optimal
72450.du2 72450dy2 \([1, -1, 1, 34870, -18782503]\) \(411664745519/13605414480\) \(-154974174311250000\) \([2]\) \(1179648\) \(1.9785\)  

Rank

sage: E.rank()
 

The elliptic curves in class 72450.du have rank \(0\).

Complex multiplication

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

Modular form 72450.2.a.du

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