Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 1155.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.l1 1155h3 \([1, 0, 1, -2054, -35989]\) \(957681397954009/31185\) \(31185\) \([2]\) \(384\) \(0.36359\)  
1155.l2 1155h4 \([1, 0, 1, -204, 151]\) \(932288503609/527295615\) \(527295615\) \([2]\) \(384\) \(0.36359\)  
1155.l3 1155h2 \([1, 0, 1, -129, -569]\) \(234770924809/1334025\) \(1334025\) \([2, 2]\) \(192\) \(0.017018\)  
1155.l4 1155h1 \([1, 0, 1, -4, -19]\) \(-4826809/144375\) \(-144375\) \([2]\) \(96\) \(-0.32956\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1155.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.