# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 1386.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1386.i1 1386i2 $$[1, -1, 1, -950, 10959]$$ $$129938649625/7072758$$ $$5156040582$$ $$$$ $$1024$$ $$0.61952$$
1386.i2 1386i1 $$[1, -1, 1, 40, 663]$$ $$9938375/274428$$ $$-200058012$$ $$$$ $$512$$ $$0.27294$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1386.2.a.i

sage: E.q_eigenform(10)

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

## 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. 