Properties

Label 145200.de
Number of curves 4
Conductor 145200
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("145200.de1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 145200.de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
145200.de1 145200kn3 [0, -1, 0, -1428808, 657756112] [2] 1966080  
145200.de2 145200kn2 [0, -1, 0, -97808, 8228112] [2, 2] 983040  
145200.de3 145200kn1 [0, -1, 0, -37308, -2661888] [2] 491520 \(\Gamma_0(N)\)-optimal
145200.de4 145200kn4 [0, -1, 0, 265192, 54692112] [2] 1966080  

Rank

sage: E.rank()
 

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

Modular form 145200.2.a.de

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{9} + 2q^{13} + 6q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.