Properties

Label 115920.ex
Number of curves $2$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ex1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.ex

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ex1 115920bu2 \([0, 0, 0, -6627, -13246]\) \(21558430658/12425175\) \(18550686873600\) \([2]\) \(229376\) \(1.2355\)  
115920.ex2 115920bu1 \([0, 0, 0, 1653, -1654]\) \(669136604/388815\) \(-290248842240\) \([2]\) \(114688\) \(0.88895\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 115920.ex have rank \(1\).

Complex multiplication

The elliptic curves in class 115920.ex do not have complex multiplication.

Modular form 115920.2.a.ex

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} + 2 q^{11} - 4 q^{13} + 6 q^{17} - 8 q^{19} + O(q^{20})\)  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.