Properties

Label 63063.w
Number of curves $6$
Conductor $63063$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("63063.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 63063.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63063.w1 63063t4 [1, -1, 0, -3027033, 2027850754] [2] 786432  
63063.w2 63063t6 [1, -1, 0, -1326978, -569398019] [2] 1572864  
63063.w3 63063t3 [1, -1, 0, -209043, 24672640] [2, 2] 786432  
63063.w4 63063t2 [1, -1, 0, -189198, 31717615] [2, 2] 393216  
63063.w5 63063t1 [1, -1, 0, -10593, 604624] [2] 196608 \(\Gamma_0(N)\)-optimal
63063.w6 63063t5 [1, -1, 0, 591372, 167626759] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 63063.w have rank \(0\).

Modular form 63063.2.a.w

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 2q^{5} - 3q^{8} - 2q^{10} + q^{11} - q^{13} - q^{16} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.