Properties

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

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

Elliptic curves in class 390.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
390.a1 390a3 \([1, 1, 0, -483, -4293]\) \(12501706118329/2570490\) \(2570490\) \([2]\) \(128\) \(0.22703\)  
390.a2 390a2 \([1, 1, 0, -33, -63]\) \(4165509529/1368900\) \(1368900\) \([2, 2]\) \(64\) \(-0.11954\)  
390.a3 390a1 \([1, 1, 0, -13, 13]\) \(273359449/9360\) \(9360\) \([2]\) \(32\) \(-0.46611\) \(\Gamma_0(N)\)-optimal
390.a4 390a4 \([1, 1, 0, 97, -297]\) \(99317171591/106616250\) \(-106616250\) \([2]\) \(128\) \(0.22703\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 390.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.