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Properties

Label 146523.u
Number of curves $2$
Conductor $146523$
CM no
Rank $1$
Graph

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

Elliptic curves in class 146523.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
146523.u1 146523bb2 \([1, 1, 0, -4787435, 3097654812]\) \(104154702625/24649677\) \(2871870647930864845317\) \([2]\) \(6193152\) \(2.8290\)  
146523.u2 146523bb1 \([1, 1, 0, -1612770, -748134369]\) \(3981876625/232713\) \(27112794788018331873\) \([2]\) \(3096576\) \(2.4824\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 146523.u have rank \(1\).

Complex multiplication

The elliptic curves in class 146523.u do not have complex multiplication.

Modular form 146523.2.a.u

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.