Properties

Label 15680bx
Number of curves $2$
Conductor $15680$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15680.t2 15680bx1 [0, 1, 0, 1055, -17025] [] 16128 \(\Gamma_0(N)\)-optimal
15680.t1 15680bx2 [0, 1, 0, -10145, 679615] [] 48384  

Rank

sage: E.rank()
 

The elliptic curves in class 15680bx have rank \(1\).

Complex multiplication

The elliptic curves in class 15680bx do not have complex multiplication.

Modular form 15680.2.a.bx

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} + q^{9} - 3q^{11} - q^{13} - 2q^{15} + 6q^{17} - q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.