Properties

Label 138600.cb
Number of curves $2$
Conductor $138600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 138600.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
138600.cb1 138600ec2 \([0, 0, 0, -5128275, -3135181250]\) \(1278763167594532/375974556419\) \(4385367226071216000000\) \([2]\) \(5898240\) \(2.8586\)  
138600.cb2 138600ec1 \([0, 0, 0, 861225, -326105750]\) \(24226243449392/29774625727\) \(-86822808619932000000\) \([2]\) \(2949120\) \(2.5120\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 138600.cb have rank \(1\).

Complex multiplication

The elliptic curves in class 138600.cb do not have complex multiplication.

Modular form 138600.2.a.cb

sage: E.q_eigenform(10)
 
\(q - q^{7} + q^{11} + 4 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.