Properties

Label 390d
Number of curves $4$
Conductor $390$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("390.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 390d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
390.d4 390d1 [1, 0, 1, 3997, 3998] [6] 720 \(\Gamma_0(N)\)-optimal
390.d3 390d2 [1, 0, 1, -16003, 27998] [6] 1440  
390.d2 390d3 [1, 0, 1, -53378, -5124652] [2] 2160  
390.d1 390d4 [1, 0, 1, -872578, -313799212] [2] 4320  

Rank

sage: E.rank()
 

The elliptic curves in class 390d have rank \(0\).

Modular form 390.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} - q^{10} + q^{12} + q^{13} - 2q^{14} + q^{15} + q^{16} - q^{18} + 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.