Properties

Label 25200bf
Number of curves $4$
Conductor $25200$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25200.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.l4 25200bf1 [0, 0, 0, 225, 6750] [2] 16384 \(\Gamma_0(N)\)-optimal
25200.l3 25200bf2 [0, 0, 0, -4275, 101250] [2, 2] 32768  
25200.l2 25200bf3 [0, 0, 0, -13275, -465750] [2] 65536  
25200.l1 25200bf4 [0, 0, 0, -67275, 6716250] [2] 65536  

Rank

sage: E.rank()
 

The elliptic curves in class 25200bf have rank \(2\).

Modular form 25200.2.a.l

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

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 Cremona 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 Cremona labels.