# Properties

 Label 384.d Number of curves $2$ Conductor $384$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 384.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
384.d1 384f2 $$[0, -1, 0, -141, 693]$$ $$19056256/27$$ $$442368$$ $$$$ $$96$$ $$-0.013528$$
384.d2 384f1 $$[0, -1, 0, -6, 18]$$ $$-219488/729$$ $$-93312$$ $$$$ $$48$$ $$-0.36010$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 384.d have rank $$0$$.

## Complex multiplication

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

## Modular form384.2.a.d

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. 