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Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 49686.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49686.h1 49686i2 \([1, 1, 0, -30428501548, 2042990125308826]\) \(-5486773802537974663600129/2635437714\) \(-1496584043449822874274\) \([]\) \(66382848\) \(4.3020\)  
49686.h2 49686i1 \([1, 1, 0, 5912462, 62524364596]\) \(40251338884511/2997011332224\) \(-1701910583588443841069184\) \([]\) \(9483264\) \(3.3290\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 49686.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - 5 q^{11} - q^{12} + q^{15} + q^{16} + 3 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.