Properties

Label 124215be
Number of curves 4
Conductor 124215
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("124215.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 124215be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
124215.t3 124215be1 [1, 1, 1, -20875, -1108528] [2] 368640 \(\Gamma_0(N)\)-optimal
124215.t2 124215be2 [1, 1, 1, -62280, 4588800] [2, 2] 737280  
124215.t4 124215be3 [1, 1, 1, 144745, 28852130] [2] 1474560  
124215.t1 124215be4 [1, 1, 1, -931785, 345782562] [2] 1474560  

Rank

sage: E.rank()
 

The elliptic curves in class 124215be have rank \(1\).

Modular form 124215.2.a.t

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + 3q^{8} + q^{9} - q^{10} + q^{12} - q^{15} - q^{16} - 2q^{17} - q^{18} - 8q^{19} + O(q^{20}) \)

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.