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Properties

Label 459186.h
Number of curves $2$
Conductor $459186$
CM no
Rank $0$
Graph

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

Elliptic curves in class 459186.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
459186.h1 459186h2 \([1, 1, 0, -3090251153, -66122191120209]\) \(-5486773802537974663600129/2635437714\) \(-1567619813330128194\) \([]\) \(188776224\) \(3.7302\)  
459186.h2 459186h1 \([1, 1, 0, 600457, -2023244139]\) \(40251338884511/2997011332224\) \(-1782692233708113995904\) \([]\) \(26968032\) \(2.7572\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 459186.h1.

Rank

sage: E.rank()
 

The elliptic curves in class 459186.h have rank \(0\).

Complex multiplication

The elliptic curves in class 459186.h do not have complex multiplication.

Modular form 459186.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - 5 q^{11} - q^{12} - q^{13} - q^{14} + q^{15} + q^{16} + 3 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.