Properties

Label 86190.t
Number of curves 4
Conductor 86190
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("86190.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 86190.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86190.t1 86190r4 [1, 1, 0, -1105432, -447803624] [2] 1769472  
86190.t2 86190r2 [1, 1, 0, -71152, -6579776] [2, 2] 884736  
86190.t3 86190r1 [1, 1, 0, -17072, 742656] [2] 442368 \(\Gamma_0(N)\)-optimal
86190.t4 86190r3 [1, 1, 0, 97848, -32909976] [2] 1769472  

Rank

sage: E.rank()
 

The elliptic curves in class 86190.t have rank \(1\).

Modular form 86190.2.a.t

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 4q^{7} - q^{8} + q^{9} - q^{10} + 4q^{11} - q^{12} - 4q^{14} - q^{15} + q^{16} + q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.