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Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 39039d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39039.d2 39039d1 \([1, 1, 1, 30241, -1913020]\) \(1392134518764179/1534746617019\) \(-3371838317590743\) \([2]\) \(207360\) \(1.6660\) \(\Gamma_0(N)\)-optimal
39039.d1 39039d2 \([1, 1, 1, -170414, -18125944]\) \(249120591156760861/80068829743287\) \(175911218946001539\) \([2]\) \(414720\) \(2.0126\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 39039.2.a.d

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.