Properties

Label 115920es
Number of curves $4$
Conductor $115920$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("es1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920es

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.es4 115920es1 \([0, 0, 0, -164307, 76750994]\) \(-164287467238609/757170892800\) \(-2260900171166515200\) \([2]\) \(1769472\) \(2.2066\) \(\Gamma_0(N)\)-optimal
115920.es3 115920es2 \([0, 0, 0, -3896787, 2955986066]\) \(2191574502231419089/4115217960000\) \(12287974985072640000\) \([2, 2]\) \(3538944\) \(2.5532\)  
115920.es2 115920es3 \([0, 0, 0, -5192787, 820437266]\) \(5186062692284555089/2903809817953800\) \(8670729655452959539200\) \([2]\) \(7077888\) \(2.8997\)  
115920.es1 115920es4 \([0, 0, 0, -62320467, 189362579474]\) \(8964546681033941529169/31696875000\) \(94646361600000000\) \([2]\) \(7077888\) \(2.8997\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.es

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.