Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26928.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
26928.e1 26928ca1 [0, 0, 0, -28227, -1824190] [2] 73728 \(\Gamma_0(N)\)-optimal
26928.e2 26928ca2 [0, 0, 0, -22467, -2590270] [2] 147456  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 26928.2.a.e

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

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.