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Properties

Label 11550.h
Number of curves $2$
Conductor $11550$
CM no
Rank $1$
Graph

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

Elliptic curves in class 11550.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.h1 11550o1 \([1, 1, 0, -2250, -42150]\) \(-2016939204025/6764142\) \(-4227588750\) \([]\) \(12000\) \(0.71163\) \(\Gamma_0(N)\)-optimal
11550.h2 11550o2 \([1, 1, 0, 16175, 827125]\) \(1197993859655/1437603552\) \(-561563887500000\) \([]\) \(60000\) \(1.5163\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11550.h have rank \(1\).

Complex multiplication

The elliptic curves in class 11550.h do not have complex multiplication.

Modular form 11550.2.a.h

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.