Properties

Label 87120.ds
Number of curves $2$
Conductor $87120$
CM no
Rank $0$
Graph

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

Elliptic curves in class 87120.ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.ds1 87120ck2 \([0, 0, 0, -257367, -50213306]\) \(5702413264/5445\) \(1800203031348480\) \([2]\) \(491520\) \(1.8488\)  
87120.ds2 87120ck1 \([0, 0, 0, -12342, -1159301]\) \(-10061824/22275\) \(-460279184151600\) \([2]\) \(245760\) \(1.5023\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 87120.ds have rank \(0\).

Complex multiplication

The elliptic curves in class 87120.ds do not have complex multiplication.

Modular form 87120.2.a.ds

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