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Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 111090.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.j1 111090h2 \([1, 1, 0, -501767, 136023069]\) \(94376601570889/456435000\) \(67568760995715000\) \([2]\) \(1622016\) \(2.0779\)  
111090.j2 111090h1 \([1, 1, 0, -15087, 4327461]\) \(-2565726409/53323200\) \(-7893747316324800\) \([2]\) \(811008\) \(1.7313\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 111090.2.a.j

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