Properties

Label 108900bw
Number of curves $4$
Conductor $108900$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 108900bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
108900.dc4 108900bw1 \([0, 0, 0, 5953200, -20542154875]\) \(72268906496/606436875\) \(-195798449820739218750000\) \([2]\) \(6635520\) \(3.1506\) \(\Gamma_0(N)\)-optimal
108900.dc3 108900bw2 \([0, 0, 0, -85931175, -282320739250]\) \(13584145739344/1195803675\) \(6177368573899944300000000\) \([2]\) \(13271040\) \(3.4972\)  
108900.dc2 108900bw3 \([0, 0, 0, -425290800, -3378477466375]\) \(-26348629355659264/24169921875\) \(-7803669978698730468750000\) \([2]\) \(19906560\) \(3.7000\)  
108900.dc1 108900bw4 \([0, 0, 0, -6806150175, -216122709888250]\) \(6749703004355978704/5671875\) \(29300179546687500000000\) \([2]\) \(39813120\) \(4.0465\)  

Rank

sage: E.rank()
 

The elliptic curves in class 108900bw have rank \(0\).

Complex multiplication

The elliptic curves in class 108900bw do not have complex multiplication.

Modular form 108900.2.a.bw

sage: E.q_eigenform(10)
 
\(q + 2q^{7} + 2q^{13} - 2q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.