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Properties

Label 49686ci
Number of curves $2$
Conductor $49686$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 49686ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49686.co2 49686ci1 \([1, 1, 1, 194431, 40553183]\) \(596183/864\) \(-1178024320065981024\) \([]\) \(907200\) \(2.1530\) \(\Gamma_0(N)\)-optimal
49686.co1 49686ci2 \([1, 1, 1, -5892104, 5530607753]\) \(-16591834777/98304\) \(-134032989305284952064\) \([]\) \(2721600\) \(2.7023\)  

Rank

sage: E.rank()
 

The elliptic curves in class 49686ci have rank \(1\).

Complex multiplication

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

Modular form 49686.2.a.ci

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