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Properties

Label 200277.h
Number of curves $2$
Conductor $200277$
CM no
Rank $1$
Graph

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

Elliptic curves in class 200277.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
200277.h1 200277l2 \([1, -1, 1, -1916, -31790]\) \(5861208627/847\) \(112355397\) \([2]\) \(90112\) \(0.55990\)  
200277.h2 200277l1 \([1, -1, 1, -131, -374]\) \(1860867/539\) \(71498889\) \([2]\) \(45056\) \(0.21332\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 200277.h have rank \(1\).

Complex multiplication

The elliptic curves in class 200277.h do not have complex multiplication.

Modular form 200277.2.a.h

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.