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Properties

Label 13650.bw
Number of curves $3$
Conductor $13650$
CM no
Rank $0$
Graph

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

Elliptic curves in class 13650.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13650.bw1 13650br3 \([1, 1, 1, -651413, -202638469]\) \(-1956469094246217097/36641439744\) \(-572522496000000\) \([]\) \(209952\) \(1.9562\)  
13650.bw2 13650br2 \([1, 1, 1, -3038, -618469]\) \(-198461344537/10417365504\) \(-162771336000000\) \([]\) \(69984\) \(1.4069\)  
13650.bw3 13650br1 \([1, 1, 1, 337, 22781]\) \(270840023/14329224\) \(-223894125000\) \([]\) \(23328\) \(0.85757\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 13650.bw have rank \(0\).

Complex multiplication

The elliptic curves in class 13650.bw do not have complex multiplication.

Modular form 13650.2.a.bw

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} + 3 q^{11} - q^{12} - q^{13} - q^{14} + q^{16} + 3 q^{17} + q^{18} - 7 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.