Properties

Label 26640.z
Number of curves $2$
Conductor $26640$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 26640.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26640.z1 26640ce2 \([0, 0, 0, -7347, 240626]\) \(14688124849/123210\) \(367903088640\) \([2]\) \(30720\) \(1.0448\)  
26640.z2 26640ce1 \([0, 0, 0, -147, 8786]\) \(-117649/11100\) \(-33144422400\) \([2]\) \(15360\) \(0.69825\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 26640.z have rank \(1\).

Complex multiplication

The elliptic curves in class 26640.z do not have complex multiplication.

Modular form 26640.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{7} - 2 q^{11} + 2 q^{13} + 2 q^{17} - 2 q^{19} + O(q^{20})\) 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 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.