Properties

Label 216384cn
Number of curves $2$
Conductor $216384$
CM no
Rank $0$
Graph

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

Elliptic curves in class 216384cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216384.k2 216384cn1 \([0, -1, 0, 9343, 1533729]\) \(2924207/34776\) \(-1072525901561856\) \([]\) \(1105920\) \(1.5650\) \(\Gamma_0(N)\)-optimal
216384.k1 216384cn2 \([0, -1, 0, -84737, -43304799]\) \(-2181825073/25039686\) \(-772248441510690816\) \([]\) \(3317760\) \(2.1143\)  

Rank

sage: E.rank()
 

The elliptic curves in class 216384cn have rank \(0\).

Complex multiplication

The elliptic curves in class 216384cn do not have complex multiplication.

Modular form 216384.2.a.cn

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + q^{9} + 5 q^{13} + 3 q^{15} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.