Properties

Label 18150.m
Number of curves 4
Conductor 18150
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("18150.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18150.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18150.m1 18150i3 [1, 1, 0, -243575, 45991125] [2] 207360  
18150.m2 18150i4 [1, 1, 0, -122575, 91850125] [2] 414720  
18150.m3 18150i1 [1, 1, 0, -16700, -790500] [2] 69120 \(\Gamma_0(N)\)-optimal
18150.m4 18150i2 [1, 1, 0, 13550, -3301250] [2] 138240  

Rank

sage: E.rank()
 

The elliptic curves in class 18150.m have rank \(0\).

Modular form 18150.2.a.m

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} + 2q^{7} - q^{8} + q^{9} - q^{12} - 4q^{13} - 2q^{14} + q^{16} - 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.