Properties

Label 115920.ds
Number of curves $2$
Conductor $115920$
CM no
Rank $0$
Graph

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

Elliptic curves in class 115920.ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ds1 115920i1 \([0, 0, 0, -87, 86]\) \(10536048/5635\) \(38949120\) \([2]\) \(30720\) \(0.14774\) \(\Gamma_0(N)\)-optimal
115920.ds2 115920i2 \([0, 0, 0, 333, 674]\) \(147704148/92575\) \(-2559513600\) \([2]\) \(61440\) \(0.49432\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.ds have rank \(0\).

Complex multiplication

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

Modular form 115920.2.a.ds

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.