Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 49686d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49686.n2 49686d1 \([1, 1, 0, 10, -762]\) \(1625/4374\) \(-253547658\) \([]\) \(18816\) \(0.29154\) \(\Gamma_0(N)\)-optimal
49686.n1 49686d2 \([1, 1, 0, -21830, 1234836]\) \(-168712375/384\) \(-2618787679872\) \([]\) \(131712\) \(1.2645\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 49686.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.