Properties

Label 11858z
Number of curves $2$
Conductor $11858$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 11858z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11858.y2 11858z1 \([1, 0, 0, -5783, -169751]\) \(73622481625/512\) \(148746752\) \([]\) \(10368\) \(0.74803\) \(\Gamma_0(N)\)-optimal
11858.y1 11858z2 \([1, 0, 0, -8478, 3268]\) \(231968823625/134217728\) \(38993068556288\) \([]\) \(31104\) \(1.2973\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11858z have rank \(1\).

Complex multiplication

The elliptic curves in class 11858z do not have complex multiplication.

Modular form 11858.2.a.z

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