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Properties

Label 180336cn
Number of curves $2$
Conductor $180336$
CM no
Rank $3$
Graph

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Show commands: SageMath
E = EllipticCurve("cn1")
 
E.isogeny_class()
 

Elliptic curves in class 180336cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180336.a2 180336cn1 \([0, -1, 0, -640, 4816]\) \(5771588/1521\) \(7652017152\) \([2]\) \(253952\) \(0.60521\) \(\Gamma_0(N)\)-optimal
180336.a1 180336cn2 \([0, -1, 0, -9480, 358416]\) \(9365216434/1053\) \(10595100672\) \([2]\) \(507904\) \(0.95178\)  

Rank

sage: E.rank()
 

The elliptic curves in class 180336cn have rank \(3\).

Complex multiplication

The elliptic curves in class 180336cn do not have complex multiplication.

Modular form 180336.2.a.cn

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} - 4 q^{7} + q^{9} - 6 q^{11} - q^{13} + 4 q^{15} - 4 q^{19} + O(q^{20})\) 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.