Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 63525.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63525.p1 63525r6 [1, 1, 1, -9223830063, 340965280222656] [2] 22118400  
63525.p2 63525r4 [1, 1, 1, -576489438, 5327401203906] [2, 2] 11059200  
63525.p3 63525r5 [1, 1, 1, -573630813, 5382852811656] [2] 22118400  
63525.p4 63525r3 [1, 1, 1, -76971188, -137100184594] [2] 11059200  
63525.p5 63525r2 [1, 1, 1, -36209313, 82361750406] [2, 2] 5529600  
63525.p6 63525r1 [1, 1, 1, 105812, 3848450156] [4] 2764800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 63525.2.a.p

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.