Properties

Label 115920.dh
Number of curves $2$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("dh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dh1 115920ei1 \([0, 0, 0, -496992, -134856601]\) \(1163923388486385664/4141725\) \(48309080400\) \([2]\) \(540672\) \(1.6920\) \(\Gamma_0(N)\)-optimal
115920.dh2 115920ei2 \([0, 0, 0, -496767, -134984806]\) \(-72646456083703504/137231087805\) \(-25610614530520320\) \([2]\) \(1081344\) \(2.0386\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.dh have rank \(1\).

Complex multiplication

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

Modular form 115920.2.a.dh

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + 2q^{13} - 2q^{17} + 6q^{19} + O(q^{20})\)  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.