Properties

Label 145200.gu
Number of curves 4
Conductor 145200
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("145200.gu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 145200.gu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
145200.gu1 145200bp3 [0, 1, 0, -3897208, -2951226412] [2] 4976640  
145200.gu2 145200bp4 [0, 1, 0, -1961208, -5882330412] [2] 9953280  
145200.gu3 145200bp1 [0, 1, 0, -267208, 50057588] [2] 1658880 \(\Gamma_0(N)\)-optimal
145200.gu4 145200bp2 [0, 1, 0, 216792, 211713588] [2] 3317760  

Rank

sage: E.rank()
 

The elliptic curves in class 145200.gu have rank \(2\).

Modular form 145200.2.a.gu

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{7} + q^{9} - 4q^{13} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.