# Properties

 Label 384.b Number of curves $2$ Conductor $384$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 384.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
384.b1 384d1 $$[0, -1, 0, -3, 3]$$ $$16000/3$$ $$768$$ $$$$ $$16$$ $$-0.72845$$ $$\Gamma_0(N)$$-optimal
384.b2 384d2 $$[0, -1, 0, 7, 9]$$ $$4000/9$$ $$-73728$$ $$$$ $$32$$ $$-0.38187$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form384.2.a.b

sage: E.q_eigenform(10)

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

## 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. 