Properties

Label 369600.wn
Number of curves $4$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("wn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.wn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.wn1 369600wn4 \([0, 1, 0, -493633, -133655137]\) \(12990838708516/144375\) \(147840000000000\) \([2]\) \(2359296\) \(1.8724\)  
369600.wn2 369600wn2 \([0, 1, 0, -31633, -1985137]\) \(13674725584/1334025\) \(341510400000000\) \([2, 2]\) \(1179648\) \(1.5258\)  
369600.wn3 369600wn1 \([0, 1, 0, -7133, 195363]\) \(2508888064/396165\) \(6338640000000\) \([2]\) \(589824\) \(1.1792\) \(\Gamma_0(N)\)-optimal
369600.wn4 369600wn3 \([0, 1, 0, 38367, -9475137]\) \(6099383804/41507235\) \(-42503408640000000\) \([2]\) \(2359296\) \(1.8724\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.wn have rank \(0\).

Complex multiplication

The elliptic curves in class 369600.wn do not have complex multiplication.

Modular form 369600.2.a.wn

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} + q^{11} + 2 q^{13} - 6 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.