Properties

Label 1155.k
Number of curves $4$
Conductor $1155$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1155.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.k1 1155f3 \([1, 1, 0, -20702, -333459]\) \(981281029968144361/522287841796875\) \(522287841796875\) \([4]\) \(4608\) \(1.5155\)  
1155.k2 1155f2 \([1, 1, 0, -16247, -803016]\) \(474334834335054841/607815140625\) \(607815140625\) \([2, 2]\) \(2304\) \(1.1689\)  
1155.k3 1155f1 \([1, 1, 0, -16242, -803529]\) \(473897054735271721/779625\) \(779625\) \([2]\) \(1152\) \(0.82233\) \(\Gamma_0(N)\)-optimal
1155.k4 1155f4 \([1, 1, 0, -11872, -1239641]\) \(-185077034913624841/551466161890875\) \(-551466161890875\) \([2]\) \(4608\) \(1.5155\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1155.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} + q^{7} - 3 q^{8} + q^{9} + q^{10} - q^{11} + q^{12} - 2 q^{13} + q^{14} - q^{15} - q^{16} - 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.