Properties

Label 39710.t
Number of curves $2$
Conductor $39710$
CM no
Rank $0$
Graph

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

Elliptic curves in class 39710.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39710.t1 39710w1 \([1, 1, 1, -31956, -2233067]\) \(-76711450249/851840\) \(-40075563271040\) \([]\) \(176904\) \(1.4250\) \(\Gamma_0(N)\)-optimal
39710.t2 39710w2 \([1, 1, 1, 107029, -11461671]\) \(2882081488391/2883584000\) \(-135660749717504000\) \([]\) \(530712\) \(1.9743\)  

Rank

sage: E.rank()
 

The elliptic curves in class 39710.t have rank \(0\).

Complex multiplication

The elliptic curves in class 39710.t do not have complex multiplication.

Modular form 39710.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 5 q^{7} + q^{8} - 2 q^{9} - q^{10} + q^{11} - q^{12} - 2 q^{13} + 5 q^{14} + q^{15} + q^{16} + 3 q^{17} - 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.