Properties

Label 54418f
Number of curves $2$
Conductor $54418$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54418f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54418.g2 54418f1 \([1, 1, 1, 5827, 807763]\) \(4533086375/60669952\) \(-292842270343168\) \([2]\) \(263424\) \(1.4567\) \(\Gamma_0(N)\)-optimal
54418.g1 54418f2 \([1, 1, 1, -102333, 11753555]\) \(24553362849625/1755162752\) \(8471835367818368\) \([2]\) \(526848\) \(1.8032\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54418f have rank \(0\).

Complex multiplication

The elliptic curves in class 54418f do not have complex multiplication.

Modular form 54418.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2q^{3} + q^{4} + 2q^{6} - q^{7} + q^{8} + q^{9} - 4q^{11} + 2q^{12} - q^{14} + q^{16} + 6q^{17} + q^{18} + 6q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.