Properties

Label 115920.cn
Number of curves $4$
Conductor $115920$
CM no
Rank $2$
Graph

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

Elliptic curves in class 115920.cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.cn1 115920ef4 \([0, 0, 0, -646707, -200170766]\) \(10017490085065009/235066440\) \(701904628776960\) \([2]\) \(1179648\) \(1.9607\)  
115920.cn2 115920ef3 \([0, 0, 0, -174387, 25121266]\) \(196416765680689/22365315000\) \(66782472744960000\) \([2]\) \(1179648\) \(1.9607\)  
115920.cn3 115920ef2 \([0, 0, 0, -41907, -2885006]\) \(2725812332209/373262400\) \(1114555554201600\) \([2, 2]\) \(589824\) \(1.6142\)  
115920.cn4 115920ef1 \([0, 0, 0, 4173, -240014]\) \(2691419471/9891840\) \(-29536875970560\) \([2]\) \(294912\) \(1.2676\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 115920.cn have rank \(2\).

Complex multiplication

The elliptic curves in class 115920.cn do not have complex multiplication.

Modular form 115920.2.a.cn

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 4q^{11} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.