Properties

Label 115920.et
Number of curves $4$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("et1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.et

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.et1 115920bt4 \([0, 0, 0, -30987, 2099466]\) \(4407931365156/100625\) \(75116160000\) \([2]\) \(163840\) \(1.2004\)  
115920.et2 115920bt3 \([0, 0, 0, -8307, -260766]\) \(84923690436/9794435\) \(7311506549760\) \([2]\) \(163840\) \(1.2004\)  
115920.et3 115920bt2 \([0, 0, 0, -2007, 30294]\) \(4790692944/648025\) \(120937017600\) \([2, 2]\) \(81920\) \(0.85380\)  
115920.et4 115920bt1 \([0, 0, 0, 198, 2511]\) \(73598976/276115\) \(-3220605360\) \([2]\) \(40960\) \(0.50723\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 115920.et have rank \(1\).

Complex multiplication

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

Modular form 115920.2.a.et

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