Properties

Label 142800bq
Number of curves 4
Conductor 142800
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("142800.in1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 142800bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
142800.in4 142800bq1 [0, 1, 0, 5592, -268812] [2] 393216 \(\Gamma_0(N)\)-optimal
142800.in3 142800bq2 [0, 1, 0, -44408, -2968812] [2, 2] 786432  
142800.in2 142800bq3 [0, 1, 0, -214408, 35451188] [4] 1572864  
142800.in1 142800bq4 [0, 1, 0, -674408, -213388812] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 142800bq have rank \(1\).

Modular form 142800.2.a.in

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

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 Cremona 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 Cremona labels.