Properties

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

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 39039.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39039.t1 39039p2 \([1, 1, 0, -28799969, -39678698730]\) \(249120591156760861/80068829743287\) \(849089854809530742459051\) \([2]\) \(5391360\) \(3.2951\)  
39039.t2 39039p1 \([1, 1, 0, 5110726, -4228458177]\) \(1392134518764179/1534746617019\) \(-16275219537891856629087\) \([2]\) \(2695680\) \(2.9485\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 39039.2.a.t

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 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.