Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 390.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
390.g1 390c4 \([1, 0, 0, -1196, -15210]\) \(189208196468929/10860320250\) \(10860320250\) \([2]\) \(288\) \(0.67982\)  
390.g2 390c2 \([1, 0, 0, -206, 1116]\) \(967068262369/4928040\) \(4928040\) \([6]\) \(96\) \(0.13052\)  
390.g3 390c1 \([1, 0, 0, -6, 36]\) \(-24137569/561600\) \(-561600\) \([6]\) \(48\) \(-0.21606\) \(\Gamma_0(N)\)-optimal
390.g4 390c3 \([1, 0, 0, 54, -960]\) \(17394111071/411937500\) \(-411937500\) \([2]\) \(144\) \(0.33325\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 390.g do not have complex multiplication.

Modular form 390.2.a.g

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.