Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ep1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.ep

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ep1 115920er1 \([0, 0, 0, -41386827, 64425512954]\) \(2625564132023811051529/918925030195200000\) \(2743895437362384076800000\) \([2]\) \(13824000\) \(3.3907\) \(\Gamma_0(N)\)-optimal
115920.ep2 115920er2 \([0, 0, 0, 123763893, 450316685306]\) \(70213095586874240921591/69970703040000000000\) \(-208931399746191360000000000\) \([2]\) \(27648000\) \(3.7373\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.ep

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