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Properties

Label 165649.m
Number of curves $2$
Conductor $165649$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 165649.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
165649.m1 165649m2 \([1, 1, 0, -417573, 405823466]\) \(-121\) \(-66548335280231987809\) \([]\) \(3409560\) \(2.4864\)  
165649.m2 165649m1 \([1, 1, 0, -41098, -3224151]\) \(-24729001\) \(-310452895489\) \([]\) \(309960\) \(1.2875\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 165649.m have rank \(0\).

Complex multiplication

The elliptic curves in class 165649.m do not have complex multiplication.

Modular form 165649.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} - q^{4} - q^{5} + 2 q^{6} + 2 q^{7} - 3 q^{8} + q^{9} - q^{10} - 2 q^{12} + q^{13} + 2 q^{14} - 2 q^{15} - q^{16} - 5 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.