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Properties

Label 54390.r
Number of curves $2$
Conductor $54390$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 54390.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54390.r1 54390u2 \([1, 0, 1, -19444, 964226]\) \(2370032608636783/196633170000\) \(67445177310000\) \([2]\) \(270336\) \(1.3957\)  
54390.r2 54390u1 \([1, 0, 1, 1276, 69122]\) \(670611173777/6387206400\) \(-2190811795200\) \([2]\) \(135168\) \(1.0491\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54390.r have rank \(2\).

Complex multiplication

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

Modular form 54390.2.a.r

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.