Properties

Label 38115.y
Number of curves $4$
Conductor $38115$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 38115.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38115.y1 38115z4 \([1, -1, 0, -2312514, -1338336455]\) \(1058993490188089/13182390375\) \(17024634924166398375\) \([2]\) \(1105920\) \(2.4999\)  
38115.y2 38115z2 \([1, -1, 0, -270639, 21143920]\) \(1697509118089/833765625\) \(1076781598340765625\) \([2, 2]\) \(552960\) \(2.1533\)  
38115.y3 38115z1 \([1, -1, 0, -221634, 40187263]\) \(932288503609/779625\) \(1006860715331625\) \([2]\) \(276480\) \(1.8067\) \(\Gamma_0(N)\)-optimal
38115.y4 38115z3 \([1, -1, 0, 987156, 161262283]\) \(82375335041831/56396484375\) \(-72834253134521484375\) \([2]\) \(1105920\) \(2.4999\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38115.y have rank \(0\).

Complex multiplication

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

Modular form 38115.2.a.y

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.