Properties

Label 32340.bl
Number of curves $2$
Conductor $32340$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32340.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.bl1 32340bj2 \([0, 1, 0, -1738340, 714049188]\) \(19288565375865424/3837216796875\) \(115569848047500000000\) \([2]\) \(829440\) \(2.5660\)  
32340.bl2 32340bj1 \([0, 1, 0, 226315, 66498900]\) \(681010157060096/1406657896875\) \(-2647870318551150000\) \([2]\) \(414720\) \(2.2194\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32340.bl have rank \(1\).

Complex multiplication

The elliptic curves in class 32340.bl do not have complex multiplication.

Modular form 32340.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - q^{11} - 2q^{13} + q^{15} - 2q^{17} + O(q^{20})\)  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.