Properties

Label 360789.m
Number of curves $6$
Conductor $360789$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("360789.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 360789.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
360789.m1 360789m3 [1, 1, 0, -5772641, 5335981026] [2] 5734400  
360789.m2 360789m6 [1, 1, 0, -2530586, -1501447371] [2] 11468800  
360789.m3 360789m4 [1, 1, 0, -398651, 64672080] [2, 2] 5734400  
360789.m4 360789m2 [1, 1, 0, -360806, 83253975] [2, 2] 2867200  
360789.m5 360789m1 [1, 1, 0, -20201, 1576896] [2] 1433600 \(\Gamma_0(N)\)-optimal
360789.m6 360789m5 [1, 1, 0, 1127764, 442307151] [2] 11468800  

Rank

sage: E.rank()
 

The elliptic curves in class 360789.m have rank \(1\).

Modular form 360789.2.a.m

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - 2q^{5} - q^{6} - 3q^{8} + q^{9} - 2q^{10} + q^{11} + q^{12} + q^{13} + 2q^{15} - q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.