Properties

Label 87120.dy
Number of curves $2$
Conductor $87120$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("dy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.dy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.dy1 87120df2 \([0, 0, 0, -11735427, -15228016254]\) \(685429074513/12500000\) \(3259626888038400000000\) \([2]\) \(4055040\) \(2.9230\)  
87120.dy2 87120df1 \([0, 0, 0, -1513347, 356566914]\) \(1469878353/640000\) \(166892896667566080000\) \([2]\) \(2027520\) \(2.5764\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 87120.dy have rank \(1\).

Complex multiplication

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

Modular form 87120.2.a.dy

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