Properties

Label 58870n
Number of curves $2$
Conductor $58870$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 58870n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58870.u2 58870n1 \([1, 1, 1, 84, 173]\) \(77882951/54880\) \(-46154080\) \([]\) \(21600\) \(0.15911\) \(\Gamma_0(N)\)-optimal
58870.u1 58870n2 \([1, 1, 1, -931, -13631]\) \(-106122119209/28672000\) \(-24113152000\) \([]\) \(64800\) \(0.70842\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58870n have rank \(1\).

Complex multiplication

The elliptic curves in class 58870n do not have complex multiplication.

Modular form 58870.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.