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Properties

Label 155771.u
Number of curves $3$
Conductor $155771$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 155771.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155771.u1 155771t1 \([0, 1, 1, -1265049, -548082755]\) \(-78843215872/539\) \(-1530631100996459\) \([]\) \(1474560\) \(2.0946\) \(\Gamma_0(N)\)-optimal
155771.u2 155771t2 \([0, 1, 1, -698609, -1039398650]\) \(-13278380032/156590819\) \(-444680478092592265139\) \([]\) \(4423680\) \(2.6439\)  
155771.u3 155771t3 \([0, 1, 1, 6240281, 26900041935]\) \(9463555063808/115539436859\) \(-328104370033398936202379\) \([]\) \(13271040\) \(3.1932\)  

Rank

sage: E.rank()
 

The elliptic curves in class 155771.u have rank \(1\).

Complex multiplication

The elliptic curves in class 155771.u do not have complex multiplication.

Modular form 155771.2.a.u

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.