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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 49686.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49686.k1 49686g2 \([1, 1, 0, -133680355, 594847722253]\) \(47490922375/384\) \(2136225562247903747712\) \([]\) \(6849024\) \(3.2641\)  
49686.k2 49686g1 \([1, 1, 0, -1728535, -875159501]\) \(12079000375/4374\) \(206826613868201418\) \([]\) \(978432\) \(2.2912\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 49686.2.a.k

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.