Properties

Label 369600.nn
Number of curves 4
Conductor 369600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("369600.nn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.nn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
369600.nn1 369600nn4 [0, 1, 0, -52785633, -147627799137] [2] 28311552  
369600.nn2 369600nn2 [0, 1, 0, -3393633, -2168359137] [2, 2] 14155776  
369600.nn3 369600nn1 [0, 1, 0, -801633, 239608863] [2] 7077888 \(\Gamma_0(N)\)-optimal
369600.nn4 369600nn3 [0, 1, 0, 4526367, -10777399137] [2] 28311552  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.nn have rank \(1\).

Modular form 369600.2.a.nn

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{7} + q^{9} - q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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 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.