Properties

Label 63525.bw
Number of curves $4$
Conductor $63525$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 63525.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63525.bw1 63525q4 \([1, 1, 0, -340375, 76286500]\) \(157551496201/13125\) \(363308408203125\) \([2]\) \(552960\) \(1.8377\)  
63525.bw2 63525q2 \([1, 1, 0, -22750, 1009375]\) \(47045881/11025\) \(305179062890625\) \([2, 2]\) \(276480\) \(1.4911\)  
63525.bw3 63525q1 \([1, 1, 0, -7625, -246000]\) \(1771561/105\) \(2906467265625\) \([2]\) \(138240\) \(1.1446\) \(\Gamma_0(N)\)-optimal
63525.bw4 63525q3 \([1, 1, 0, 52875, 6378750]\) \(590589719/972405\) \(-26916793346953125\) \([2]\) \(552960\) \(1.8377\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63525.bw have rank \(1\).

Complex multiplication

The elliptic curves in class 63525.bw do not have complex multiplication.

Modular form 63525.2.a.bw

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.