Properties

Label 63525.z
Number of curves 6
Conductor 63525
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("63525.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 63525.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63525.z1 63525bv6 [1, 0, 0, -13670038, 19452573317] [2] 2457600  
63525.z2 63525bv4 [1, 0, 0, -859163, 300315192] [2, 2] 1228800  
63525.z3 63525bv2 [1, 0, 0, -118038, -8733933] [2, 2] 614400  
63525.z4 63525bv1 [1, 0, 0, -102913, -12711808] [2] 307200 \(\Gamma_0(N)\)-optimal
63525.z5 63525bv5 [1, 0, 0, 93712, 930165567] [2] 2457600  
63525.z6 63525bv3 [1, 0, 0, 381087, -63138558] [2] 1228800  

Rank

sage: E.rank()
 

The elliptic curves in class 63525.z have rank \(0\).

Modular form 63525.2.a.z

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} - q^{6} + q^{7} + 3q^{8} + q^{9} - q^{12} + 6q^{13} - q^{14} - q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.