Properties

Label 127296dj
Number of curves $2$
Conductor $127296$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("dj1")
 
E.isogeny_class()
 

Elliptic curves in class 127296dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127296.b2 127296dj1 \([0, 0, 0, -151212, -22611760]\) \(2000852317801/2094417\) \(400249321684992\) \([2]\) \(1179648\) \(1.7192\) \(\Gamma_0(N)\)-optimal
127296.b1 127296dj2 \([0, 0, 0, -188652, -10556080]\) \(3885442650361/1996623837\) \(381560757203238912\) \([2]\) \(2359296\) \(2.0658\)  

Rank

sage: E.rank()
 

The elliptic curves in class 127296dj have rank \(0\).

Complex multiplication

The elliptic curves in class 127296dj do not have complex multiplication.

Modular form 127296.2.a.dj

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.