Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("dt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.dt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.dt1 87120gc1 \([0, 0, 0, -115797, 15797639]\) \(-68679424/3375\) \(-8438451709446000\) \([]\) \(456192\) \(1.8175\) \(\Gamma_0(N)\)-optimal
87120.dt2 87120gc2 \([0, 0, 0, 602943, 37934831]\) \(9695350016/5859375\) \(-14650089773343750000\) \([]\) \(1368576\) \(2.3668\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 87120.2.a.dt

sage: E.q_eigenform(10)
 
\(q + q^{5} - 2q^{7} - 4q^{13} + 3q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.