Properties

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

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Show commands: SageMath
E = EllipticCurve("cq1")
 
E.isogeny_class()
 

Elliptic curves in class 111090.cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.cq1 111090cq4 \([1, 0, 0, -255168451, 1535392465481]\) \(12411881707829361287041/303132494474220600\) \(44874488304278834103113400\) \([2]\) \(65691648\) \(3.7062\)  
111090.cq2 111090cq2 \([1, 0, 0, -31401451, -66911610319]\) \(23131609187144855041/322060536000000\) \(47676517758576504000000\) \([2]\) \(21897216\) \(3.1569\)  
111090.cq3 111090cq1 \([1, 0, 0, -253931, -2803784655]\) \(-12232183057921/22933241856000\) \(-3394942845804969984000\) \([2]\) \(10948608\) \(2.8104\) \(\Gamma_0(N)\)-optimal
111090.cq4 111090cq3 \([1, 0, 0, 2285269, 75681363825]\) \(8915971454369279/16719623332762560\) \(-2475104303810648395515840\) \([2]\) \(32845824\) \(3.3597\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 111090.2.a.cq

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.