Properties

Label 115520cw
Number of curves $2$
Conductor $115520$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 115520cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115520.cx2 115520cw1 \([0, -1, 0, -405, 3275]\) \(318767104/125\) \(2888000\) \([]\) \(36288\) \(0.20435\) \(\Gamma_0(N)\)-optimal
115520.cx1 115520cw2 \([0, -1, 0, -1165, -11013]\) \(7575076864/1953125\) \(45125000000\) \([]\) \(108864\) \(0.75365\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115520cw have rank \(0\).

Complex multiplication

The elliptic curves in class 115520cw do not have complex multiplication.

Modular form 115520.2.a.cw

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{5} + 4 q^{7} + q^{9} + 3 q^{11} + 2 q^{13} + 2 q^{15} + 6 q^{17} + O(q^{20})\) 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.