Properties

Label 3600.bm
Number of curves $2$
Conductor $3600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3600.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.bm1 3600bq1 \([0, 0, 0, -120, 475]\) \(131072/9\) \(13122000\) \([2]\) \(768\) \(0.11405\) \(\Gamma_0(N)\)-optimal
3600.bm2 3600bq2 \([0, 0, 0, 105, 2050]\) \(5488/81\) \(-1889568000\) \([2]\) \(1536\) \(0.46063\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3600.bm have rank \(0\).

Complex multiplication

The elliptic curves in class 3600.bm do not have complex multiplication.

Modular form 3600.2.a.bm

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