Properties

Label 183456.ce
Number of curves $2$
Conductor $183456$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 183456.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
183456.ce1 183456cz2 \([0, 0, 0, -14700, 241472]\) \(1000000/507\) \(178108102029312\) \([2]\) \(368640\) \(1.4269\)  
183456.ce2 183456cz1 \([0, 0, 0, -8085, -277144]\) \(10648000/117\) \(642216714048\) \([2]\) \(184320\) \(1.0804\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 183456.ce have rank \(1\).

Complex multiplication

The elliptic curves in class 183456.ce do not have complex multiplication.

Modular form 183456.2.a.ce

sage: E.q_eigenform(10)
 
\(q - q^{13} + 2 q^{17} + 2 q^{19} + O(q^{20})\) 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.