Properties

Label 38115y
Number of curves $3$
Conductor $38115$
CM no
Rank $0$
Graph

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

Elliptic curves in class 38115y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38115.q2 38115y1 \([0, 0, 1, -1452, 23625]\) \(-262144/35\) \(-45201378915\) \([]\) \(27000\) \(0.77710\) \(\Gamma_0(N)\)-optimal
38115.q3 38115y2 \([0, 0, 1, 9438, -60228]\) \(71991296/42875\) \(-55371689170875\) \([]\) \(81000\) \(1.3264\)  
38115.q1 38115y3 \([0, 0, 1, -143022, -21778155]\) \(-250523582464/13671875\) \(-17656788638671875\) \([]\) \(243000\) \(1.8757\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 38115.2.a.y

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