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Properties

Label 54418.c
Number of curves $2$
Conductor $54418$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 54418.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54418.c1 54418c2 \([1, 1, 0, -1322597, -585981235]\) \(53008645999484449/2060047808\) \(9943457300084672\) \([2]\) \(1677312\) \(2.1542\)  
54418.c2 54418c1 \([1, 1, 0, -78757, -10083315]\) \(-11192824869409/2563305472\) \(-12372585921998848\) \([2]\) \(838656\) \(1.8076\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54418.c have rank \(1\).

Complex multiplication

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

Modular form 54418.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 4 q^{5} - 2 q^{6} + q^{7} - q^{8} + q^{9} + 4 q^{10} + 4 q^{11} + 2 q^{12} - q^{14} - 8 q^{15} + q^{16} - q^{18} - 8 q^{19} + O(q^{20})\) 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.