Properties

Label 25200j
Number of curves $2$
Conductor $25200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25200.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.k1 25200j1 [0, 0, 0, -675, 3250] [2] 18432 \(\Gamma_0(N)\)-optimal
25200.k2 25200j2 [0, 0, 0, 2325, 24250] [2] 36864  

Rank

sage: E.rank()
 

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

Modular form 25200.2.a.k

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

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 Cremona 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 Cremona labels.