# Properties

 Label 1386.j Number of curves $2$ Conductor $1386$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 1386.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1386.j1 1386j2 $$[1, -1, 1, -4070120, -3114601045]$$ $$10228636028672744397625/167006381634183168$$ $$121747652211319529472$$ $$$$ $$66560$$ $$2.6532$$
1386.j2 1386j1 $$[1, -1, 1, -15080, -136579669]$$ $$-520203426765625/11054534935707648$$ $$-8058755968130875392$$ $$$$ $$33280$$ $$2.3067$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1386.j have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1386.j do not have complex multiplication.

## Modular form1386.2.a.j

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} + q^{11} + 6q^{13} - q^{14} + q^{16} - 4q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 