Properties

 Label 1386.f Number of curves $2$ Conductor $1386$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

Elliptic curves in class 1386.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1386.f1 1386h2 $$[1, -1, 1, -2111, 37851]$$ $$1426487591593/2156$$ $$1571724$$ $$$$ $$768$$ $$0.45699$$
1386.f2 1386h1 $$[1, -1, 1, -131, 627]$$ $$-338608873/13552$$ $$-9879408$$ $$$$ $$384$$ $$0.11042$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form1386.2.a.f

sage: E.q_eigenform(10)

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