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Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 11858q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11858.t2 11858q1 \([1, 1, 0, 17664, 350288]\) \(24167/16\) \(-403505727852304\) \([]\) \(63360\) \(1.4914\) \(\Gamma_0(N)\)-optimal
11858.t1 11858q2 \([1, 1, 0, -308431, 67591077]\) \(-128667913/4096\) \(-103297466330189824\) \([]\) \(190080\) \(2.0407\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11858.2.a.q

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