Properties

Label 63504by
Number of curves $2$
Conductor $63504$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 63504by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63504.cp1 63504by1 \([0, 0, 0, -4851, 142002]\) \(-35937/4\) \(-1405192126464\) \([]\) \(82944\) \(1.0683\) \(\Gamma_0(N)\)-optimal
63504.cp2 63504by2 \([0, 0, 0, 30429, -203742]\) \(109503/64\) \(-1821128995897344\) \([]\) \(248832\) \(1.6176\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63504by have rank \(1\).

Complex multiplication

The elliptic curves in class 63504by do not have complex multiplication.

Modular form 63504.2.a.by

sage: E.q_eigenform(10)
 
\(q + 3 q^{5} + q^{13} + 3 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.