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Properties

Label 58989f
Number of curves $2$
Conductor $58989$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 58989f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58989.b2 58989f1 \([0, -1, 1, -1254, -27178]\) \(-1466003456/1361367\) \(-202676234859\) \([]\) \(91520\) \(0.86613\) \(\Gamma_0(N)\)-optimal
58989.b1 58989f2 \([0, -1, 1, -19804, 3098868]\) \(-5770012921856/24407490807\) \(-3633714008873739\) \([]\) \(457600\) \(1.6708\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58989f have rank \(0\).

Complex multiplication

The elliptic curves in class 58989f do not have complex multiplication.

Modular form 58989.2.a.f

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.