Properties

Label 119952.bz
Number of curves $2$
Conductor $119952$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bz1 119952l2 \([0, 0, 0, -254751, 48942670]\) \(2248430329584/28647703\) \(23296022394027264\) \([2]\) \(1032192\) \(1.9494\)  
119952.bz2 119952l1 \([0, 0, 0, -2646, 2000719]\) \(-40310784/34000561\) \(-1728057024470448\) \([2]\) \(516096\) \(1.6028\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 119952.bz have rank \(1\).

Complex multiplication

The elliptic curves in class 119952.bz do not have complex multiplication.

Modular form 119952.2.a.bz

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