# Properties

 Label 1386.g Number of curves $4$ Conductor $1386$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 1386.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1386.g1 1386g3 [1, -1, 1, -828041, -289811415]  15360
1386.g2 1386g2 [1, -1, 1, -51881, -4494999] [2, 2] 7680
1386.g3 1386g4 [1, -1, 1, -13001, -11104599]  15360
1386.g4 1386g1 [1, -1, 1, -5801, 57705]  3840 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1386.g have rank $$1$$.

## Complex multiplication

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

## Modular form1386.2.a.g

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - 2q^{5} - q^{7} + q^{8} - 2q^{10} - q^{11} + 2q^{13} - q^{14} + q^{16} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 