Properties

Label 26928bw
Number of curves $2$
Conductor $26928$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 26928bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26928.bu2 26928bw1 \([0, 0, 0, -78699, 8314778]\) \(18052771191337/444958272\) \(1328638280859648\) \([2]\) \(129024\) \(1.6856\) \(\Gamma_0(N)\)-optimal
26928.bu1 26928bw2 \([0, 0, 0, -176619, -16498150]\) \(204055591784617/78708537864\) \(235022434725298176\) \([2]\) \(258048\) \(2.0322\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26928bw have rank \(1\).

Complex multiplication

The elliptic curves in class 26928bw do not have complex multiplication.

Modular form 26928.2.a.bw

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