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Properties

Label 39039o
Number of curves $2$
Conductor $39039$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 39039o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39039.s2 39039o1 \([1, 1, 0, -1459, -23408]\) \(-156503678869/11647251\) \(-25589010447\) \([2]\) \(31104\) \(0.74587\) \(\Gamma_0(N)\)-optimal
39039.s1 39039o2 \([1, 1, 0, -23754, -1419075]\) \(674733819141829/3361743\) \(7385749371\) \([2]\) \(62208\) \(1.0924\)  

Rank

sage: E.rank()
 

The elliptic curves in class 39039o have rank \(0\).

Complex multiplication

The elliptic curves in class 39039o do not have complex multiplication.

Modular form 39039.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - 3 q^{8} + q^{9} + 2 q^{10} + q^{11} + q^{12} + q^{14} - 2 q^{15} - q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.