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Properties

Label 54390.s
Number of curves $2$
Conductor $54390$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 54390.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54390.s1 54390q2 \([1, 0, 1, -2997097129, -63154028153044]\) \(25306840319912277316429470841/75096378453196800\) \(8835013828640150323200\) \([2]\) \(27525120\) \(3.8647\)  
54390.s2 54390q1 \([1, 0, 1, -187241129, -987650066644]\) \(-6170768047181777430174841/10643549045391360000\) \(-1252202901641248112640000\) \([2]\) \(13762560\) \(3.5181\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 54390.2.a.s

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