Properties

Label 15680.br
Number of curves $2$
Conductor $15680$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.br1 15680dp2 \([0, -1, 0, -157845, -24085235]\) \(-225637236736/1715\) \(-3305767485440\) \([]\) \(55296\) \(1.5771\)  
15680.br2 15680dp1 \([0, -1, 0, -1045, -63475]\) \(-65536/875\) \(-1686616064000\) \([]\) \(18432\) \(1.0278\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15680.br have rank \(0\).

Complex multiplication

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

Modular form 15680.2.a.br

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.