Properties

Label 119025.co
Number of curves $2$
Conductor $119025$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("co1")
 
E.isogeny_class()
 

Elliptic curves in class 119025.co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119025.co1 119025bs2 \([0, 0, 1, -991875, -389724219]\) \(-102400/3\) \(-3161664934013671875\) \([]\) \(2851200\) \(2.3287\)  
119025.co2 119025bs1 \([0, 0, 1, 7935, 1201491]\) \(20480/243\) \(-655602840717075\) \([]\) \(570240\) \(1.5240\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 119025.co have rank \(1\).

Complex multiplication

The elliptic curves in class 119025.co do not have complex multiplication.

Modular form 119025.2.a.co

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} - 3 q^{7} + 2 q^{11} - q^{13} - 6 q^{14} - 4 q^{16} - 2 q^{17} + 5 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.