Properties

Label 38646x
Number of curves $2$
Conductor $38646$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 38646x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38646.v1 38646x1 \([1, -1, 1, -3922241, 2990829521]\) \(9153747013124116391113/5485837418496\) \(3999175478083584\) \([2]\) \(870912\) \(2.3166\) \(\Gamma_0(N)\)-optimal
38646.v2 38646x2 \([1, -1, 1, -3899201, 3027684305]\) \(-8993380100968273380553/224220843480310272\) \(-163456994897146188288\) \([2]\) \(1741824\) \(2.6631\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38646x have rank \(1\).

Complex multiplication

The elliptic curves in class 38646x do not have complex multiplication.

Modular form 38646.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 2 q^{5} + q^{8} - 2 q^{10} + 4 q^{11} + 4 q^{13} + q^{16} + 2 q^{17} - q^{19} + O(q^{20})\) 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.