Properties

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

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

Elliptic curves in class 115920.dt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dt1 115920ed1 \([0, 0, 0, -90912, 10550059]\) \(7124261256822784/475453125\) \(5545685250000\) \([2]\) \(552960\) \(1.5009\) \(\Gamma_0(N)\)-optimal
115920.dt2 115920ed2 \([0, 0, 0, -85287, 11912434]\) \(-367624742361424/115740505125\) \(-21599956028448000\) \([2]\) \(1105920\) \(1.8475\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.dt

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + 4 q^{11} + 6 q^{13} + 6 q^{17} - 6 q^{19} + O(q^{20})\) Copy content 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.