Properties

Label 273999.h
Number of curves 2
Conductor 273999
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("273999.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 273999.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
273999.h1 273999h2 [1, 0, 1, -446926, 114068945] [2] 2280960  
273999.h2 273999h1 [1, 0, 1, -8311, 4239749] [2] 1140480 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 273999.h have rank \(1\).

Modular form 273999.2.a.h

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

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.