Properties

Label 346560ik
Number of curves $4$
Conductor $346560$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("346560.ik1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 346560ik

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
346560.ik4 346560ik1 [0, 1, 0, -231521, -73243905] [2] 6635520 \(\Gamma_0(N)\)-optimal
346560.ik3 346560ik2 [0, 1, 0, -4390241, -3540784641] [2, 2] 13271040  
346560.ik2 346560ik3 [0, 1, 0, -5083361, -2348756865] [2] 26542080  
346560.ik1 346560ik4 [0, 1, 0, -70236641, -226588880001] [2] 26542080  

Rank

sage: E.rank()
 

The elliptic curves in class 346560ik have rank \(1\).

Modular form 346560.2.a.ik

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + 4q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} - 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.