Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.f1 72450m2 \([1, -1, 0, -1523382, 724085576]\) \(158909194494247023/5080516\) \(12499974553500\) \([2]\) \(884736\) \(2.0155\)  
72450.f2 72450m1 \([1, -1, 0, -95082, 11363876]\) \(-38638468208943/219395344\) \(-539794819494000\) \([2]\) \(442368\) \(1.6689\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 72450.2.a.f

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.