Properties

Label 267696.dn
Number of curves $2$
Conductor $267696$
CM no
Rank $0$
Graph

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

Elliptic curves in class 267696.dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
267696.dn1 267696dn1 \([0, 0, 0, -12675, 162578]\) \(62500/33\) \(118905389171712\) \([2]\) \(602112\) \(1.3923\) \(\Gamma_0(N)\)-optimal
267696.dn2 267696dn2 \([0, 0, 0, 48165, 1269866]\) \(1714750/1089\) \(-7847755685332992\) \([2]\) \(1204224\) \(1.7389\)  

Rank

sage: E.rank()
 

The elliptic curves in class 267696.dn have rank \(0\).

Complex multiplication

The elliptic curves in class 267696.dn do not have complex multiplication.

Modular form 267696.2.a.dn

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} - q^{11} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.