Properties

Label 128271e
Number of curves 2
Conductor 128271
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("128271.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 128271e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
128271.m2 128271e1 [1, 1, 0, -3890, -1359873] [2] 368640 \(\Gamma_0(N)\)-optimal
128271.m1 128271e2 [1, 1, 0, -209225, -36636426] [2] 737280  

Rank

sage: E.rank()
 

The elliptic curves in class 128271e have rank \(0\).

Modular form 128271.2.a.m

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - q^{6} + 2q^{7} - 3q^{8} + q^{9} - q^{11} + q^{12} + 2q^{14} - q^{16} + q^{18} - 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.