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Properties

Label 13650.j
Number of curves $2$
Conductor $13650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 13650.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13650.j1 13650f2 \([1, 1, 0, -91862400, -338925189750]\) \(-5486773802537974663600129/2635437714\) \(-41178714281250\) \([]\) \(1152480\) \(2.8513\)  
13650.j2 13650f1 \([1, 1, 0, 17850, -10363500]\) \(40251338884511/2997011332224\) \(-46828302066000000\) \([]\) \(164640\) \(1.8783\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 13650.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 5 q^{11} - q^{12} + q^{13} + q^{14} + q^{16} + 3 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.