# Properties

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

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 $$[1, -1, 1, -4453952, 2135383395]$$ $$13403946614821979039929/5057590268826067968$$ $$3686983305974203548672$$ $$$$ $$5058560$$ $$2.8378$$ $$\Gamma_0(N)$$-optimal
38646.p2 38646be2 $$[1, -1, 1, 13933408, 15227183715]$$ $$410363075617640914325831/374944243169850027552$$ $$-273334353270820670085408$$ $$$$ $$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)

$$q + q^{2} + q^{4} - 4q^{5} - 4q^{7} + q^{8} - 4q^{10} - 4q^{14} + q^{16} + 6q^{17} + q^{19} + O(q^{20})$$ ## 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. 