Properties

Label 1155.h
Number of curves $2$
Conductor $1155$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1155.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.h1 1155j2 \([0, 1, 1, -841, -9674]\) \(-65860951343104/3493875\) \(-3493875\) \([]\) \(432\) \(0.32335\)  
1155.h2 1155j1 \([0, 1, 1, -1, -35]\) \(-262144/509355\) \(-509355\) \([3]\) \(144\) \(-0.22596\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1155.h have rank \(1\).

Complex multiplication

The elliptic curves in class 1155.h do not have complex multiplication.

Modular form 1155.2.a.h

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.