Properties

Label 54080.da
Number of curves $2$
Conductor $54080$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("da1")
 
E.isogeny_class()
 

Elliptic curves in class 54080.da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54080.da1 54080p1 \([0, -1, 0, -11041, 98721]\) \(117649/65\) \(82245736202240\) \([2]\) \(172032\) \(1.3606\) \(\Gamma_0(N)\)-optimal
54080.da2 54080p2 \([0, -1, 0, 43039, 736865]\) \(6967871/4225\) \(-5345972853145600\) \([2]\) \(344064\) \(1.7072\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54080.da have rank \(1\).

Complex multiplication

The elliptic curves in class 54080.da do not have complex multiplication.

Modular form 54080.2.a.da

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