Properties

Label 145200cl
Number of curves $2$
Conductor $145200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cl1")
 
E.isogeny_class()
 

Elliptic curves in class 145200cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145200.iu1 145200cl1 \([0, 1, 0, -45173, 3861603]\) \(-56197120/3267\) \(-592659434188800\) \([]\) \(622080\) \(1.5909\) \(\Gamma_0(N)\)-optimal
145200.iu2 145200cl2 \([0, 1, 0, 245227, 6939843]\) \(8990228480/5314683\) \(-964125197328691200\) \([]\) \(1866240\) \(2.1402\)  

Rank

sage: E.rank()
 

The elliptic curves in class 145200cl have rank \(0\).

Complex multiplication

The elliptic curves in class 145200cl do not have complex multiplication.

Modular form 145200.2.a.cl

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - q^{13} - 6 q^{17} - 7 q^{19} + O(q^{20})\) 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.