# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 384.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
384.f1 384c2 [0, 1, 0, -13, 11]  32
384.f2 384c1 [0, 1, 0, 2, 2]  16 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form384.2.a.f

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{7} + q^{9} + 4q^{11} + 6q^{13} + 6q^{17} + O(q^{20})$$

## 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. 