Properties

Label 48400.k
Number of curves $2$
Conductor $48400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 48400.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48400.k1 48400bd2 \([0, 1, 0, -27628, -1106052]\) \(41141648/14641\) \(829997587232000\) \([2]\) \(184320\) \(1.5637\)  
48400.k2 48400bd1 \([0, 1, 0, -24603, -1493252]\) \(464857088/121\) \(428717762000\) \([2]\) \(92160\) \(1.2171\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 48400.k have rank \(1\).

Complex multiplication

The elliptic curves in class 48400.k do not have complex multiplication.

Modular form 48400.2.a.k

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