Properties

Label 110466.l
Number of curves $4$
Conductor $110466$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 110466.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
110466.l1 110466q3 \([1, -1, 0, -2438442, -1107438476]\) \(46753267515625/11591221248\) \(397537708083519946752\) \([2]\) \(3981312\) \(2.6630\)  
110466.l2 110466q1 \([1, -1, 0, -830187, 291246277]\) \(1845026709625/793152\) \(27202295728438848\) \([2]\) \(1327104\) \(2.1136\) \(\Gamma_0(N)\)-optimal
110466.l3 110466q2 \([1, -1, 0, -700227, 385415293]\) \(-1107111813625/1228691592\) \(-42139756370317830408\) \([2]\) \(2654208\) \(2.4602\)  
110466.l4 110466q4 \([1, -1, 0, 5878998, -7027792268]\) \(655215969476375/1001033261568\) \(-34331884449861331026432\) \([2]\) \(7962624\) \(3.0095\)  

Rank

sage: E.rank()
 

The elliptic curves in class 110466.l have rank \(0\).

Complex multiplication

The elliptic curves in class 110466.l do not have complex multiplication.

Modular form 110466.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{7} - q^{8} - 2 q^{13} - 2 q^{14} + q^{16} + q^{17} + O(q^{20})\) 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.