Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bm1 119952ba1 \([0, 0, 0, -4746, 123235]\) \(2955053056/70227\) \(280960810704\) \([2]\) \(143360\) \(0.98187\) \(\Gamma_0(N)\)-optimal
119952.bm2 119952ba2 \([0, 0, 0, 609, 385630]\) \(390224/1003833\) \(-64257390118656\) \([2]\) \(286720\) \(1.3284\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 119952.2.a.bm

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