Properties

Label 390b
Number of curves 6
Conductor 390
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("390.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 390b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
390.f6 390b1 [1, 1, 1, 15, 15] [4] 64 \(\Gamma_0(N)\)-optimal
390.f5 390b2 [1, 1, 1, -65, 47] [2, 4] 128  
390.f3 390b3 [1, 1, 1, -565, -5353] [2, 2] 256  
390.f2 390b4 [1, 1, 1, -845, 9095] [4] 256  
390.f1 390b5 [1, 1, 1, -9015, -333213] [2] 512  
390.f4 390b6 [1, 1, 1, -115, -13093] [2] 512  

Rank

sage: E.rank()
 

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

Modular form 390.2.a.f

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.