Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.h1 72450d1 \([1, -1, 0, -3792, 77616]\) \(14295828483/2254000\) \(950906250000\) \([2]\) \(110592\) \(1.0212\) \(\Gamma_0(N)\)-optimal
72450.h2 72450d2 \([1, -1, 0, 6708, 424116]\) \(79119341757/231437500\) \(-97637695312500\) \([2]\) \(221184\) \(1.3678\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 72450.2.a.h

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