# Properties

 Label 384.g Number of curves $2$ Conductor $384$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("g1")

E.isogeny_class()

## Elliptic curves in class 384.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
384.g1 384a1 $$[0, 1, 0, -3, -3]$$ $$16000/3$$ $$768$$ $$[2]$$ $$16$$ $$-0.72845$$ $$\Gamma_0(N)$$-optimal
384.g2 384a2 $$[0, 1, 0, 7, -9]$$ $$4000/9$$ $$-73728$$ $$[2]$$ $$32$$ $$-0.38187$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form384.2.a.g

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.