Properties

Label 111090bs
Number of curves $2$
Conductor $111090$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 111090bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.bs1 111090bs1 \([1, 1, 1, -129616, -17200591]\) \(1626794704081/83462400\) \(12355430582073600\) \([2]\) \(1622016\) \(1.8456\) \(\Gamma_0(N)\)-optimal
111090.bs2 111090bs2 \([1, 1, 1, 81984, -67646031]\) \(411664745519/13605414480\) \(-2014089627760272720\) \([2]\) \(3244032\) \(2.1922\)  

Rank

sage: E.rank()
 

The elliptic curves in class 111090bs have rank \(1\).

Complex multiplication

The elliptic curves in class 111090bs do not have complex multiplication.

Modular form 111090.2.a.bs

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.