Properties

Label 139650.dn
Number of curves $2$
Conductor $139650$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("dn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 139650.dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.dn1 139650gr1 \([1, 0, 1, -32903526, -72140372552]\) \(6248109436056487/50429952000\) \(31797351000576000000000\) \([2]\) \(18579456\) \(3.1450\) \(\Gamma_0(N)\)-optimal
139650.dn2 139650gr2 \([1, 0, 1, -10951526, -166885204552]\) \(-230380217865127/18948168000000\) \(-11947295700655875000000000\) \([2]\) \(37158912\) \(3.4915\)  

Rank

sage: E.rank()
 

The elliptic curves in class 139650.dn have rank \(0\).

Complex multiplication

The elliptic curves in class 139650.dn do not have complex multiplication.

Modular form 139650.2.a.dn

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{12} - 6q^{13} + q^{16} + 2q^{17} - q^{18} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.