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Properties

Label 11858.x
Number of curves $2$
Conductor $11858$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 11858.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11858.x1 11858bm2 \([1, 0, 0, -1390474, -631206696]\) \(1426487591593/2156\) \(449358651471884\) \([2]\) \(184320\) \(2.0796\)  
11858.x2 11858bm1 \([1, 0, 0, -86094, -10060940]\) \(-338608873/13552\) \(-2824540094966128\) \([2]\) \(92160\) \(1.7330\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11858.x have rank \(0\).

Complex multiplication

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

Modular form 11858.2.a.x

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