Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("dq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dq1 115920cm1 \([0, 0, 0, -2427, -39254]\) \(14295828483/2254000\) \(249274368000\) \([2]\) \(110592\) \(0.90963\) \(\Gamma_0(N)\)-optimal
115920.dq2 115920cm2 \([0, 0, 0, 4293, -218006]\) \(79119341757/231437500\) \(-25595136000000\) \([2]\) \(221184\) \(1.2562\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.dq

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