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Properties

Label 36518a
Number of curves $3$
Conductor $36518$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 36518a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36518.a2 36518a1 \([1, 1, 0, -14915, -707579]\) \(-413493625/152\) \(-134900559512\) \([]\) \(60480\) \(1.1036\) \(\Gamma_0(N)\)-optimal
36518.a3 36518a2 \([1, 1, 0, 9110, -2661292]\) \(94196375/3511808\) \(-3116742526965248\) \([]\) \(181440\) \(1.6529\)  
36518.a1 36518a3 \([1, 1, 0, -82185, 72912709]\) \(-69173457625/2550136832\) \(-2263255825453678592\) \([]\) \(544320\) \(2.2022\)  

Rank

sage: E.rank()
 

The elliptic curves in class 36518a have rank \(1\).

Complex multiplication

The elliptic curves in class 36518a do not have complex multiplication.

Modular form 36518.2.a.a

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