Properties

Label 1150.h
Number of curves $2$
Conductor $1150$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1150.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1150.h1 1150e2 \([1, -1, 1, -4255, -105753]\) \(545138290809/16928\) \(264500000\) \([2]\) \(800\) \(0.71281\)  
1150.h2 1150e1 \([1, -1, 1, -255, -1753]\) \(-116930169/23552\) \(-368000000\) \([2]\) \(400\) \(0.36624\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1150.h have rank \(0\).

Complex multiplication

The elliptic curves in class 1150.h do not have complex multiplication.

Modular form 1150.2.a.h

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