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Properties

Label 110946u
Number of curves $2$
Conductor $110946$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 110946u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
110946.x2 110946u1 \([1, 1, 1, -14807964, 21752402301]\) \(1096869734297/10036224\) \(3285678427131096843264\) \([2]\) \(12595200\) \(2.9507\) \(\Gamma_0(N)\)-optimal
110946.x1 110946u2 \([1, 1, 1, -25835324, -15017226883]\) \(5825198645657/3073907232\) \(1006341695759746255025952\) \([2]\) \(25190400\) \(3.2973\)  

Rank

sage: E.rank()
 

The elliptic curves in class 110946u have rank \(0\).

Complex multiplication

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

Modular form 110946.2.a.u

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