Properties

Label 59248.z
Number of curves 6
Conductor 59248
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("59248.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 59248.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
59248.z1 59248bb6 [0, -1, 0, -23111128, -42756445200] [2] 1824768  
59248.z2 59248bb5 [0, -1, 0, -1443288, -668832784] [2] 912384  
59248.z3 59248bb4 [0, -1, 0, -300648, -51908752] [2] 608256  
59248.z4 59248bb2 [0, -1, 0, -89048, 10250864] [2] 202752  
59248.z5 59248bb1 [0, -1, 0, -4408, 229488] [2] 101376 \(\Gamma_0(N)\)-optimal
59248.z6 59248bb3 [0, -1, 0, 37912, -4781200] [2] 304128  

Rank

sage: E.rank()
 

The elliptic curves in class 59248.z have rank \(0\).

Modular form 59248.2.a.z

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + q^{7} + q^{9} - 4q^{13} - 6q^{17} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.