Properties

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

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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 15680bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.dn2 15680bu1 \([0, -1, 0, -4545, 140225]\) \(-115501303/25600\) \(-2301834035200\) \([2]\) \(30720\) \(1.0925\) \(\Gamma_0(N)\)-optimal
15680.dn1 15680bu2 \([0, -1, 0, -76225, 8125377]\) \(544737993463/20000\) \(1798307840000\) \([2]\) \(61440\) \(1.4391\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 15680.2.a.bu

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{5} + q^{9} + 4 q^{11} + 2 q^{13} + 2 q^{15} - 8 q^{17} - 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.