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Properties

Label 155526.k
Number of curves $2$
Conductor $155526$
CM no
Rank $1$
Graph

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

Elliptic curves in class 155526.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155526.k1 155526db1 \([1, 1, 0, -413816344, -3240280139060]\) \(1311889499494111/438012\) \(2616588239316550093476\) \([2]\) \(28385280\) \(3.4677\) \(\Gamma_0(N)\)-optimal
155526.k2 155526db2 \([1, 1, 0, -412001874, -3270100953510]\) \(-1294708239486271/23981814018\) \(-143262130984940092442951214\) \([2]\) \(56770560\) \(3.8143\)  

Rank

sage: E.rank()
 

The elliptic curves in class 155526.k have rank \(1\).

Complex multiplication

The elliptic curves in class 155526.k do not have complex multiplication.

Modular form 155526.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.