Properties

Label 111090.be
Number of curves $2$
Conductor $111090$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 111090.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.be1 111090be1 \([1, 0, 1, -12443, -295594]\) \(1439069689/579600\) \(85801601264400\) \([2]\) \(405504\) \(1.3715\) \(\Gamma_0(N)\)-optimal
111090.be2 111090be2 \([1, 0, 1, 40457, -2136514]\) \(49471280711/41992020\) \(-6216326011605780\) \([2]\) \(811008\) \(1.7181\)  

Rank

sage: E.rank()
 

The elliptic curves in class 111090.be have rank \(0\).

Complex multiplication

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

Modular form 111090.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 2q^{11} + q^{12} + 4q^{13} + q^{14} + q^{15} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20})\)  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 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.