Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ek1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ek1 115920bv1 \([0, 0, 0, -9499647, 10855002814]\) \(508017439289666674384/21234429931640625\) \(3962854251562500000000\) \([2]\) \(6881280\) \(2.9092\) \(\Gamma_0(N)\)-optimal
115920.ek2 115920bv2 \([0, 0, 0, 4562853, 40248440314]\) \(14073614784514581404/945607964406328125\) \(-705892562997466320000000\) \([2]\) \(13762560\) \(3.2557\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.ek

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.