Properties

Label 134640.fd
Number of curves $2$
Conductor $134640$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("fd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 134640.fd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
134640.fd1 134640be2 [0, 0, 0, -20667, 730474] [2] 393216  
134640.fd2 134640be1 [0, 0, 0, 3813, 79306] [2] 196608 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 134640.fd have rank \(1\).

Complex multiplication

The elliptic curves in class 134640.fd do not have complex multiplication.

Modular form 134640.2.a.fd

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

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.