Properties

Label 366597o
Number of curves 6
Conductor 366597
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("366597.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 366597o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
366597.o4 366597o1 [1, -1, 0, -161973, 25123144] [2] 2027520 \(\Gamma_0(N)\)-optimal
366597.o3 366597o2 [1, -1, 0, -185778, 17272255] [2, 2] 4055040  
366597.o6 366597o3 [1, -1, 0, 599787, 124580434] [2] 8110080  
366597.o2 366597o4 [1, -1, 0, -1352223, -592778480] [2, 2] 8110080  
366597.o5 366597o5 [1, -1, 0, 147492, -1836642101] [2] 16220160  
366597.o1 366597o6 [1, -1, 0, -21515058, -38406159239] [2] 16220160  

Rank

sage: E.rank()
 

The elliptic curves in class 366597o have rank \(1\).

Modular form 366597.2.a.o

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 2q^{5} - q^{7} - 3q^{8} - 2q^{10} - q^{11} + 6q^{13} - q^{14} - q^{16} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.