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Properties

Label 38514.x
Number of curves $2$
Conductor $38514$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 38514.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38514.x1 38514w2 \([1, 1, 1, -11125206, 14278041105]\) \(1294373635812597347281/2083292441154\) \(245097272409326946\) \([]\) \(1386000\) \(2.6010\)  
38514.x2 38514w1 \([1, 1, 1, -104616, -12422775]\) \(1076291879750641/60150618144\) \(7076660074023456\) \([]\) \(277200\) \(1.7963\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38514.x have rank \(1\).

Complex multiplication

The elliptic curves in class 38514.x do not have complex multiplication.

Modular form 38514.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - 3 q^{11} - q^{12} - 4 q^{13} + q^{15} + q^{16} + 7 q^{17} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.