Properties

Label 289800.cp
Number of curves $2$
Conductor $289800$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 289800.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289800.cp1 289800cp2 \([0, 0, 0, -109875, -14017250]\) \(12576878500/1127\) \(13145328000000\) \([2]\) \(1105920\) \(1.5573\)  
289800.cp2 289800cp1 \([0, 0, 0, -6375, -251750]\) \(-9826000/3703\) \(-10797948000000\) \([2]\) \(552960\) \(1.2107\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 289800.cp have rank \(0\).

Complex multiplication

The elliptic curves in class 289800.cp do not have complex multiplication.

Modular form 289800.2.a.cp

sage: E.q_eigenform(10)
 
\(q + q^{7} - 4q^{11} - 6q^{13} + O(q^{20})\)  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.