# Properties

 Label 384.e Number of curves $2$ Conductor $384$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 384.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
384.e1 384h1 $$[0, 1, 0, -35, 69]$$ $$19056256/27$$ $$6912$$ $$$$ $$48$$ $$-0.36010$$ $$\Gamma_0(N)$$-optimal
384.e2 384h2 $$[0, 1, 0, -25, 119]$$ $$-219488/729$$ $$-5971968$$ $$$$ $$96$$ $$-0.013528$$

## Rank

sage: E.rank()

The elliptic curves in class 384.e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 384.e do not have complex multiplication.

## Modular form384.2.a.e

sage: E.q_eigenform(10)

$$q + q^{3} - 4q^{5} - 2q^{7} + q^{9} - 4q^{11} + 2q^{13} - 4q^{15} - 2q^{17} - 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 