Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("346560.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 346560.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
346560.b1 346560b3 [0, -1, 0, -70236641, 226588880001] [2] 26542080  
346560.b2 346560b4 [0, -1, 0, -5083361, 2348756865] [2] 26542080  
346560.b3 346560b2 [0, -1, 0, -4390241, 3540784641] [2, 2] 13271040  
346560.b4 346560b1 [0, -1, 0, -231521, 73243905] [2] 6635520 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 346560.2.a.b

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.