Properties

Label 15870d
Number of curves $2$
Conductor $15870$
CM no
Rank $0$
Graph

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

Elliptic curves in class 15870d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15870.a2 15870d1 \([1, 1, 0, -6623, 372657]\) \(-217081801/285660\) \(-42287932051740\) \([2]\) \(76032\) \(1.3075\) \(\Gamma_0(N)\)-optimal
15870.a1 15870d2 \([1, 1, 0, -128293, 17625463]\) \(1577505447721/838350\) \(124105887543150\) \([2]\) \(152064\) \(1.6541\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15870d have rank \(0\).

Complex multiplication

The elliptic curves in class 15870d do not have complex multiplication.

Modular form 15870.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} - 2 q^{11} - q^{12} + 4 q^{13} + 4 q^{14} + q^{15} + q^{16} + 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.