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Properties

Label 72450fb
Number of curves $2$
Conductor $72450$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("fb1")
 
E.isogeny_class()
 

Elliptic curves in class 72450fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.fb2 72450fb1 \([1, -1, 1, 3820, -183553]\) \(21653735/63112\) \(-17972128125000\) \([]\) \(207360\) \(1.2267\) \(\Gamma_0(N)\)-optimal
72450.fb1 72450fb2 \([1, -1, 1, -35555, 5958947]\) \(-17455277065/43606528\) \(-12417640200000000\) \([3]\) \(622080\) \(1.7761\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 72450.2.a.fb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} + 6 q^{11} - q^{13} + q^{14} + q^{16} + 3 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.