Properties

Label 25200.s
Number of curves $4$
Conductor $25200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25200.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.s1 25200bg4 [0, 0, 0, -651675, 202464250] [2] 294912  
25200.s2 25200bg2 [0, 0, 0, -44175, 2596750] [2, 2] 147456  
25200.s3 25200bg1 [0, 0, 0, -16050, -750125] [2] 73728 \(\Gamma_0(N)\)-optimal
25200.s4 25200bg3 [0, 0, 0, 113325, 16929250] [2] 294912  

Rank

sage: E.rank()
 

The elliptic curves in class 25200.s have rank \(0\).

Modular form 25200.2.a.s

sage: E.q_eigenform(10)
 
\( q - q^{7} - 4q^{11} + 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.