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Properties

Label 13650n
Number of curves $2$
Conductor $13650$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 13650n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13650.k2 13650n1 \([1, 1, 0, -345, -17775]\) \(-36495256013/1053197964\) \(-131649745500\) \([2]\) \(21120\) \(0.81409\) \(\Gamma_0(N)\)-optimal
13650.k1 13650n2 \([1, 1, 0, -12495, -540225]\) \(1726143065560493/9662982966\) \(1207872870750\) \([2]\) \(42240\) \(1.1607\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 13650.2.a.n

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