Properties

Label 39270.j
Number of curves $2$
Conductor $39270$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 39270.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39270.j1 39270i2 \([1, 1, 0, -414178793, -2525377035003]\) \(7857552442072520325669578770969/1792478631174686569867737600\) \(1792478631174686569867737600\) \([2]\) \(21288960\) \(3.9420\)  
39270.j2 39270i1 \([1, 1, 0, 59106327, -244237413627]\) \(22836293554064983709494580711/38990271813074615296327680\) \(-38990271813074615296327680\) \([2]\) \(10644480\) \(3.5954\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 39270.j have rank \(0\).

Complex multiplication

The elliptic curves in class 39270.j do not have complex multiplication.

Modular form 39270.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} - q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + O(q^{20})\) 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.