Properties

Label 132834.be
Number of curves $2$
Conductor $132834$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 132834.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
132834.be1 132834i2 \([1, 0, 0, -24424, -1249288]\) \(333822098953/53954184\) \(260426540918856\) \([]\) \(1050624\) \(1.4882\)  
132834.be2 132834i1 \([1, 0, 0, -6679, 209351]\) \(6826561273/7074\) \(34144846866\) \([]\) \(350208\) \(0.93890\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 132834.be have rank \(1\).

Complex multiplication

The elliptic curves in class 132834.be do not have complex multiplication.

Modular form 132834.2.a.be

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 3 q^{5} + q^{6} - 5 q^{7} + q^{8} + q^{9} + 3 q^{10} - 3 q^{11} + q^{12} - 5 q^{14} + 3 q^{15} + q^{16} - 3 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.