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Properties

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

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 111090m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.h2 111090m1 \([1, 1, 0, -1496287, -666285839]\) \(205692449327/12757500\) \(22978205078614222500\) \([2]\) \(5087232\) \(2.4667\) \(\Gamma_0(N)\)-optimal
111090.h1 111090m2 \([1, 1, 0, -4538037, 2899253511]\) \(5738223173327/1302030450\) \(2345155610323367548350\) \([2]\) \(10174464\) \(2.8132\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 111090.2.a.m

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.