Properties

Label 390.a
Number of curves $4$
Conductor $390$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("390.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 390.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
390.a1 390a3 [1, 1, 0, -483, -4293] [2] 128  
390.a2 390a2 [1, 1, 0, -33, -63] [2, 2] 64  
390.a3 390a1 [1, 1, 0, -13, 13] [2] 32 \(\Gamma_0(N)\)-optimal
390.a4 390a4 [1, 1, 0, 97, -297] [2] 128  

Rank

sage: E.rank()
 

The elliptic curves in class 390.a have rank \(1\).

Modular form 390.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.