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Properties

Label 63525.o
Number of curves $2$
Conductor $63525$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 63525.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63525.o1 63525bd2 \([1, 1, 1, -216810888, -1228733900844]\) \(244738769070151/28588707\) \(131661475897120189453125\) \([2]\) \(13939200\) \(3.4624\)  
63525.o2 63525bd1 \([1, 1, 1, -14665263, -15860150844]\) \(75740658391/20253807\) \(93276205956268822265625\) \([2]\) \(6969600\) \(3.1158\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 63525.2.a.o

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.