Properties

Label 265200j
Number of curves 4
Conductor 265200
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("265200.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 265200j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.j3 265200j1 [0, -1, 0, -83408, -9242688] [2] 1179648 \(\Gamma_0(N)\)-optimal
265200.j2 265200j2 [0, -1, 0, -91408, -7354688] [2, 2] 2359296  
265200.j1 265200j3 [0, -1, 0, -559408, 155509312] [2] 4718592  
265200.j4 265200j4 [0, -1, 0, 248592, -49514688] [2] 4718592  

Rank

sage: E.rank()
 

The elliptic curves in class 265200j have rank \(1\).

Modular form 265200.2.a.j

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

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.