Properties

Label 48139.g
Number of curves $3$
Conductor $48139$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 48139.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48139.g1 48139h3 \([0, 1, 1, -62069, 14648769]\) \(-178643795968/524596891\) \(-77659167125821099\) \([]\) \(449064\) \(1.9279\)  
48139.g2 48139h1 \([0, 1, 1, -3879, -94461]\) \(-43614208/91\) \(-13471265899\) \([]\) \(49896\) \(0.82924\) \(\Gamma_0(N)\)-optimal
48139.g3 48139h2 \([0, 1, 1, 6701, -460000]\) \(224755712/753571\) \(-111555552909619\) \([]\) \(149688\) \(1.3785\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48139.g have rank \(1\).

Complex multiplication

The elliptic curves in class 48139.g do not have complex multiplication.

Modular form 48139.2.a.g

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 2 q^{4} + 3 q^{5} - q^{7} + q^{9} + 4 q^{12} + q^{13} - 6 q^{15} + 4 q^{16} + 6 q^{17} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.