Properties

Label 63525bj
Number of curves $6$
Conductor $63525$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("63525.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 63525bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63525.t4 63525bj1 [1, 0, 0, -801688, -276349633] [2] 737280 \(\Gamma_0(N)\)-optimal
63525.t3 63525bj2 [1, 0, 0, -816813, -265384008] [2, 2] 1474560  
63525.t5 63525bj3 [1, 0, 0, 771312, -1172203383] [2] 2949120  
63525.t2 63525bj4 [1, 0, 0, -2646938, 1343295867] [2, 2] 2949120  
63525.t6 63525bj5 [1, 0, 0, 5505437, 7987481492] [2] 5898240  
63525.t1 63525bj6 [1, 0, 0, -40081313, 97661942742] [2] 5898240  

Rank

sage: E.rank()
 

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

Modular form 63525.2.a.t

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.