Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.bh1 115920dl2 \([0, 0, 0, -573123, 166896322]\) \(6972359126281921/5071500000\) \(15143417856000000\) \([2]\) \(1474560\) \(2.0393\)  
115920.bh2 115920dl1 \([0, 0, 0, -43203, 1455298]\) \(2986606123201/1421952000\) \(4245925920768000\) \([2]\) \(737280\) \(1.6927\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 115920.bh have rank \(2\).

Complex multiplication

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

Modular form 115920.2.a.bh

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} - 2q^{11} - 6q^{13} - 4q^{17} + 2q^{19} + O(q^{20})\)  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.