Properties

Label 111090.n
Number of curves $4$
Conductor $111090$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 111090.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.n1 111090p4 \([1, 1, 0, -66465422, -116975783364]\) \(219353215817909485369/87028564162480920\) \(12883350864186403437737880\) \([2]\) \(38928384\) \(3.5165\)  
111090.n2 111090p2 \([1, 1, 0, -30176022, 62504331156]\) \(20527812941011798969/474091398849600\) \(70182541695954113294400\) \([2, 2]\) \(19464192\) \(3.1699\)  
111090.n3 111090p1 \([1, 1, 0, -30006742, 63254343124]\) \(20184279492242626489/11148103680\) \(1650319438932971520\) \([2]\) \(9732096\) \(2.8233\) \(\Gamma_0(N)\)-optimal
111090.n4 111090p3 \([1, 1, 0, 3404898, 193987065324]\) \(29489595518609351/109830613939935000\) \(-16258872574014070327215000\) \([2]\) \(38928384\) \(3.5165\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 111090.2.a.n

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.