Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("oq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 388080.oq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.oq1 388080oq2 \([0, 0, 0, -189032592, 18912291835696]\) \(-2126464142970105856/438611057788643355\) \(-154083201246162036370538311680\) \([]\) \(460800000\) \(4.2799\)  
388080.oq2 388080oq1 \([0, 0, 0, -63082992, -225841753424]\) \(-79028701534867456/16987307596875\) \(-5967607721237710732800000\) \([]\) \(92160000\) \(3.4752\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 388080.2.a.oq

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.