Properties

Label 54390.i
Number of curves $4$
Conductor $54390$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 54390.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54390.i1 54390i4 \([1, 1, 0, -513888, 63078912]\) \(127568139540190201/59114336463360\) \(6954742570577840640\) \([2]\) \(1741824\) \(2.3101\)  
54390.i2 54390i2 \([1, 1, 0, -260313, -51226083]\) \(16581570075765001/998001000\) \(117413819649000\) \([2]\) \(580608\) \(1.7608\)  
54390.i3 54390i1 \([1, 1, 0, -15313, -903083]\) \(-3375675045001/999000000\) \(-117531351000000\) \([2]\) \(290304\) \(1.4142\) \(\Gamma_0(N)\)-optimal
54390.i4 54390i3 \([1, 1, 0, 113312, 7508992]\) \(1367594037332999/995878502400\) \(-117164109928857600\) \([2]\) \(870912\) \(1.9635\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54390.i have rank \(1\).

Complex multiplication

The elliptic curves in class 54390.i do not have complex multiplication.

Modular form 54390.2.a.i

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