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Properties

Label 110946n
Number of curves $2$
Conductor $110946$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 110946n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
110946.o1 110946n1 \([1, 0, 1, -42901, 3274400]\) \(1838265625/86592\) \(411321026436672\) \([2]\) \(645120\) \(1.5650\) \(\Gamma_0(N)\)-optimal
110946.o2 110946n2 \([1, 0, 1, 24339, 12607312]\) \(335702375/14644872\) \(-69564668596102152\) \([2]\) \(1290240\) \(1.9116\)  

Rank

sage: E.rank()
 

The elliptic curves in class 110946n have rank \(1\).

Complex multiplication

The elliptic curves in class 110946n do not have complex multiplication.

Modular form 110946.2.a.n

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