Properties

Label 38115.u
Number of curves $4$
Conductor $38115$
CM no
Rank $1$
Graph

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

Elliptic curves in class 38115.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38115.u1 38115j4 \([1, -1, 0, -22545045, -11667888050]\) \(981281029968144361/522287841796875\) \(674518018278803466796875\) \([2]\) \(4423680\) \(3.2637\)  
38115.u2 38115j2 \([1, -1, 0, -17693550, -28610278889]\) \(474334834335054841/607815140625\) \(784973785190418140625\) \([2, 2]\) \(2211840\) \(2.9172\)  
38115.u3 38115j1 \([1, -1, 0, -17688105, -28628790800]\) \(473897054735271721/779625\) \(1006860715331625\) \([2]\) \(1105920\) \(2.5706\) \(\Gamma_0(N)\)-optimal
38115.u4 38115j3 \([1, -1, 0, -12929175, -44367972764]\) \(-185077034913624841/551466161890875\) \(-712200884069433535882875\) \([2]\) \(4423680\) \(3.2637\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38115.u have rank \(1\).

Complex multiplication

The elliptic curves in class 38115.u do not have complex multiplication.

Modular form 38115.2.a.u

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