Properties

Label 17600e
Number of curves 3
Conductor 17600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17600.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17600e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17600.bj3 17600e1 [0, -1, 0, -33, 187] [] 2240 \(\Gamma_0(N)\)-optimal
17600.bj2 17600e2 [0, -1, 0, -1033, -22813] [] 11200  
17600.bj1 17600e3 [0, -1, 0, -782033, -265925813] [] 56000  

Rank

sage: E.rank()
 

The elliptic curves in class 17600e have rank \(1\).

Modular form 17600.2.a.bj

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{7} - 2q^{9} - q^{11} + 4q^{13} + 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.