Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.bj1 115920bb2 \([0, 0, 0, -10083, 386818]\) \(75933869762/648025\) \(967496140800\) \([2]\) \(221184\) \(1.1247\)  
115920.bj2 115920bb1 \([0, 0, 0, -1083, -3782]\) \(188183524/100625\) \(75116160000\) \([2]\) \(110592\) \(0.77813\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 115920.bj have rank \(2\).

Complex multiplication

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

Modular form 115920.2.a.bj

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