Properties

Label 49686.l
Number of curves $2$
Conductor $49686$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 49686.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49686.l1 49686f2 \([1, 1, 0, -42713570, 107429494866]\) \(531373116625/2058\) \(33378524410123496058\) \([]\) \(3773952\) \(2.9595\)  
49686.l2 49686f1 \([1, 1, 0, -728900, 24312072]\) \(2640625/1512\) \(24522997525805017512\) \([]\) \(1257984\) \(2.4102\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 49686.l have rank \(0\).

Complex multiplication

The elliptic curves in class 49686.l do not have complex multiplication.

Modular form 49686.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.