Properties

Label 63426.u
Number of curves $2$
Conductor $63426$
CM no
Rank $1$
Graph

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

Elliptic curves in class 63426.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63426.u1 63426v2 \([1, 1, 1, -98953229, 73424872451]\) \(120737856347074599697/67244278190817024\) \(59679544420538129197465344\) \([2]\) \(20643840\) \(3.6363\)  
63426.u2 63426v1 \([1, 1, 1, -60820749, -181559394813]\) \(28035534600833657617/183328572506112\) \(162704782931649794998272\) \([2]\) \(10321920\) \(3.2897\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 63426.u have rank \(1\).

Complex multiplication

The elliptic curves in class 63426.u do not have complex multiplication.

Modular form 63426.2.a.u

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.