Properties

Label 388080ds
Number of curves $2$
Conductor $388080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ds1")
 
E.isogeny_class()
 

Elliptic curves in class 388080ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.ds2 388080ds1 \([0, 0, 0, -9408, 20354992]\) \(-262144/509355\) \(-178935408893767680\) \([]\) \(3981312\) \(1.9895\) \(\Gamma_0(N)\)-optimal
388080.ds1 388080ds2 \([0, 0, 0, -5936448, 5567471728]\) \(-65860951343104/3493875\) \(-1227391410212352000\) \([]\) \(11943936\) \(2.5388\)  

Rank

sage: E.rank()
 

The elliptic curves in class 388080ds have rank \(0\).

Complex multiplication

The elliptic curves in class 388080ds do not have complex multiplication.

Modular form 388080.2.a.ds

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{11} + 4 q^{13} + 3 q^{17} - q^{19} + O(q^{20})\) 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.