Properties

Label 38646.p
Number of curves $2$
Conductor $38646$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38646.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38646.p1 38646be1 \([1, -1, 1, -4453952, 2135383395]\) \(13403946614821979039929/5057590268826067968\) \(3686983305974203548672\) \([2]\) \(5058560\) \(2.8378\) \(\Gamma_0(N)\)-optimal
38646.p2 38646be2 \([1, -1, 1, 13933408, 15227183715]\) \(410363075617640914325831/374944243169850027552\) \(-273334353270820670085408\) \([2]\) \(10117120\) \(3.1844\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38646.p have rank \(0\).

Complex multiplication

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

Modular form 38646.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 4q^{5} - 4q^{7} + q^{8} - 4q^{10} - 4q^{14} + q^{16} + 6q^{17} + q^{19} + O(q^{20})\)  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.