Properties

Label 25200.cw
Number of curves $4$
Conductor $25200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25200.cw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.cw1 25200dy4 [0, 0, 0, -963675, -364101750] [2] 294912  
25200.cw2 25200dy3 [0, 0, 0, -315675, 63794250] [2] 294912  
25200.cw3 25200dy2 [0, 0, 0, -63675, -5001750] [2, 2] 147456  
25200.cw4 25200dy1 [0, 0, 0, 8325, -465750] [2] 73728 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 25200.cw have rank \(1\).

Modular form 25200.2.a.cw

sage: E.q_eigenform(10)
 
\( q - q^{7} + 4q^{11} + 6q^{13} + 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.