Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("390.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 390.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
390.c1 390g4 [1, 0, 1, -86529, 9789652] [2] 1280  
390.c2 390g3 [1, 0, 1, -6209, 104276] [2] 1280  
390.c3 390g2 [1, 0, 1, -5409, 152596] [2, 2] 640  
390.c4 390g1 [1, 0, 1, -289, 3092] [2] 320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 390.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 4q^{7} - q^{8} + q^{9} + q^{10} + q^{12} - q^{13} - 4q^{14} - q^{15} + q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.