Properties

Label 138600.di
Number of curves $4$
Conductor $138600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("di1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 138600.di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
138600.di1 138600bf4 \([0, 0, 0, -6699675, -6673558250]\) \(1425631925916578/270703125\) \(6314962500000000000\) \([2]\) \(3145728\) \(2.6086\)  
138600.di2 138600bf3 \([0, 0, 0, -2937675, 1876675750]\) \(120186986927618/4332064275\) \(101058395407200000000\) \([2]\) \(3145728\) \(2.6086\)  
138600.di3 138600bf2 \([0, 0, 0, -462675, -81049250]\) \(939083699236/300155625\) \(3501015210000000000\) \([2, 2]\) \(1572864\) \(2.2620\)  
138600.di4 138600bf1 \([0, 0, 0, 81825, -8630750]\) \(20777545136/23059575\) \(-67241720700000000\) \([2]\) \(786432\) \(1.9154\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 138600.di have rank \(0\).

Complex multiplication

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

Modular form 138600.2.a.di

sage: E.q_eigenform(10)
 
\(q + q^{7} - q^{11} + 2 q^{13} - 2 q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.