Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ws1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.ws

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.ws1 369600ws4 \([0, 1, 0, -78848033, -269511167937]\) \(13235378341603461121/9240\) \(37847040000000\) \([2]\) \(14155776\) \(2.8184\)  
369600.ws2 369600ws2 \([0, 1, 0, -4928033, -4212287937]\) \(3231355012744321/85377600\) \(349706649600000000\) \([2, 2]\) \(7077888\) \(2.4718\)  
369600.ws3 369600ws3 \([0, 1, 0, -4736033, -4555391937]\) \(-2868190647517441/527295615000\) \(-2159802839040000000000\) \([2]\) \(14155776\) \(2.8184\)  
369600.ws4 369600ws1 \([0, 1, 0, -320033, -60479937]\) \(885012508801/127733760\) \(523197480960000000\) \([2]\) \(3538944\) \(2.1253\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.ws

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} + q^{11} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.