Properties

Label 17745n
Number of curves 4
Conductor 17745
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("17745.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17745n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17745.f3 17745n1 [1, 0, 0, -426, 3171] [2] 7680 \(\Gamma_0(N)\)-optimal
17745.f2 17745n2 [1, 0, 0, -1271, -13560] [2, 2] 15360  
17745.f1 17745n3 [1, 0, 0, -19016, -1010829] [2] 30720  
17745.f4 17745n4 [1, 0, 0, 2954, -83695] [2] 30720  

Rank

sage: E.rank()
 

The elliptic curves in class 17745n have rank \(0\).

Modular form 17745.2.a.f

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

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.